- Jul 2019
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Apparently the martian climate experiences periodic changes at intervals similar to those between ice ages on Earth.
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Climate Change on Mars
skip
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clear that it was frozen water.
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It discovered numerous sedimentary rocks
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differential galactic rotation
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21-cm line that comes from cool hydrogen
Wavelength \(\lambda = 21\, cm\) is a radio wavelength outside the FM band and the AM band.
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The ages of stony meteorites can be determined from the careful measurement of radioactive isotopes and their decay products.
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rocks from the sky
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we know the precise way light is dimmed by distance
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the type Ia supernova
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the universe is expanding.
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Variation of Hubble’s Constant
Bypass
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There are also thousands of stars within a parsec of Sagittarius A*.
There are only a few stars within a parsec of our solar system.
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First, an asteroid might have ventured too close to the black hole and been heated to a very high temperature
Nifty. This is like seeing a mega-Chelyabinsk event crush into the black hole... seeing it from halfway across the galaxy.
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One of the stars has been observed for its full orbit of 15.6 years.
S2
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Note that the age of these surfaces is not necessarily the age of the planet as a whole. On geologically active objects (including Earth), vast outpourings of molten rock or the erosive effects of water and ice, which we call planet weathering, have erased evidence of earlier epochs
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metallic iron-nickel core
Earth also has iron/nickel core
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Brahe didn’t have the ability to analyze them
...but Kepler did!!!
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Otherwise the pre-telescopic observations of Brahe would not have been sufficient for Kepler to deduce that its orbit had the shape of an ellipse rather than a circle.
This is the part that always astounds me, that Kepler spotted this small amount of eccentricity!
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original (unshifted) wavelength
i.e., in the lab on Earth
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It is the pattern of lines
I.e., its quantum fingerprints!
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in the direction of Sagittarius.
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We know that this extensive dark matter halo exists because of its effects on the orbits of distant star clusters and other dwarf galaxies that are associated with the Galaxy.
In other words, they are orbiting faster than they would if only the visible stars were present. The visible stars do not have enough mass to control these visible star clusters.
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philosophical tradition, going back to the Greeks and defended by the Catholic Church, held that pure human thought combined with divine revelation represented the path to truth
Galileo broke out of this tradition by his emphasis on
- observation of the physical universe and
- his insight that the physical universe was like a book written in a mathematical language.
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in those days, before the telescope, no one imagined testing these predictions.
Galileo observed the phases of Venus in the century after Copernicus.
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ooops should be Ry^2
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Huge. Fig. 2 is one to keep in mind all of the semester.
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Analyzing vectors using perpendicular components is very useful in many areas of physics,
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The person taking the walk ends up at the tip of
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The angles that vectors and make
The angles here are not that helpful. Main thing is to build resultant from four components Ax, Ay, Bx, By, then get the trig on the resultant R
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Figure 6. To add vectors A and B
Lovely diagram
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Calculate the momentum of a 2000-kg elephant charging a hunter at a speed of (b) Compare the elephant’s momentum with the momentum of a 0.0400-kg tranquilizer dart fired at a speed of (c) What is the momentum of the 90.0-kg hunter running at after missing the elephant?
Basic momentum calculations.
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Linear momentum is defined as
Sir Isaac Newton used the term "quantity of motion," and it is his second definition on page 1 of the Principia.
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most broadly applicable form
They say that half the Ph.D.s on the planet are at NASA working out spaceflight trajectories using this most general form, $$\vec{F}_{net}=\frac{\Delta \vec{p}}{\Delta t}$$ because, e.g., a rocket boosting a spacecraft into orbit is always losing mass through the rocket motor -- the "flames" blazing out of the rocket, hundreds of kg per sec of fuel oxidized and violently expelled. So \(\frac{\Delta m}{\Delta t}\) is not negligible and must be included in calculations... not easy
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State Newton’s second law of motion in terms of momentum.
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What is the mass of a large ship that has a momentum of when the ship is moving at a speed of (b) Compare the ship’s momentum to the momentum of a 1100-kg artillery shell fired at a speed of 3
Battleship recoil problem. I like it.
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This quantity was the average force
57 gram tennis ball. That is a ton of g's of acceleration.
$$a=\frac{F}{m}=\frac{661\,N}{0.057 \, kg}=11596 \frac{m}{s^2}=1183 \times g$$
So about 1200 g's!!!
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A runaway train car that has a mass of 15,000 kg travels at a speed of down a track. Compute the time required for a force of 1500 N to bring the car to rest
Classic stopping time problem. Use the impulse equation, though: \(F_{net} \Delta t = \Delta p\)
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Example 2: Calculating Force: Venus Williams’ Racquet
Good.
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when the mass of the system is constant
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Compare the player’s momentum with the momentum of a hard-thrown 0.410-kg football
Poor comparison. A better comparison is with another player of similar though different mass and with velocity \(v=8.00 \frac{m}{s}\) and antiparallel to the first player's velocity.
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Astrology, that unlikely and vague pseudoscience, makes much of the position of the planets at the moment of one’s birth. The only known force a planet exerts on Earth is gravitational. (a) Calculate the magnitude of the gravitational force exerted on a 4.20 kg baby by a 100 kg father 0.200 m away at birth (he is assisting, so he is close to the child). (b) Calculate the magnitude of the force on the baby due to Jupiter if it is at its closest distance to Earth, some away. How does the force of Jupiter on the baby compare to the force of the father on the baby? Other objects in the room and the hospital building also exert similar gravitational forces. (Of course, there could be an unknown force acting, but scientists first need to be convinced that there is even an effect, much less that an unknown force causes it.)
Another good calculation for study.
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aching feet
:D
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Figure 2.
Good concise diagram
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The Cavendish Experiment: Then and Now
Did not discuss in lecture, although it will definitely come up in PHY2054C when the topic is the Coulomb interaction between electrical charges
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gravity is able to supply the necessary centripetal force
- "gravity"
- "is able to supply"
- "the necessary centripetal force."
$$1 \longrightarrow 2 \longrightarrow 3$$
$$F \left[ 1 \right] \,= \left[ 2 \right] \frac{mv^2}{r} \left[ 3 \right]$$
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Tides
Did not talk too much about tides in lecture -- a few minutes
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The gravitational force is relatively simple. It is always attractive, and it depends only on the masses involved and the distance between them. Stated in modern language, Newton’s universal law of gravitation states that every particle in the universe attracts every other particle with a force along a line joining them. The force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
A lovely paragraph, right on the money
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”Weightlessness” and Microgravity
Did not discuss in lecture
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2: (a) Calculate the magnitude of the acceleration due to gravity on the surface of Earth due to the Moon. (b) Calculate the magnitude of the acceleration due to gravity at Earth due to the Sun. (c) Take the ratio of the Moon’s acceleration to the Sun’s and comment on why the tides are predominantly due to the Moon in spite of this number.
A nice study workout, similar to HW 07.
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to show that the motion of heavenly bodies should be conic sections
Kepler's first law of planetary motion, before Newton, had discovered this conic section idea, but Newton SHOWED or PROVED as in geometric analysis that conic sections were required, no coincidence.
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Recall that the acceleration due to gravity is about on Earth.
We reviewed a bunch of this section in the Geospatial energy levels mini-lecture in YouTube.
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an equation for
Excellent.
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3: Draw a free body diagram for a satellite
nice study task
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torque is analogous to force, angular acceleration is analogous to translational acceleration, and is analogous to mass (or inertia). The quantity is called the rotational inertia or moment of inertia of a point mass a distance from the center of rotation.
Big topic during most recent lectures
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the sum of for all the point masses of which it is composed. That is,
Critical definition
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Why is the moment of inertia of a hoop that has a mass and a radius greater than the moment of inertia of a disk that has the same mass and radius?
We actually discussed the answer to this question in Friday lecture.
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Calculate the moment of inertia of a skater given the following information. (a) The 60.0-kg skater is approximated as a cylinder that has a 0.110-m radius. (b) The skater with arms extended is approximately a cylinder that is 52.5 kg, has a 0.110-m radius, and has two 0.900-m-long arms which are 3.75 kg each and extend straight out from the cylinder like rods rotated about their ends.
This would not be a brain burner, to make you think, but a rotational torture device. I will not put ANYTHING like this on Exam 3.
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radians (rad), defined
Nice definition of radians system for measuring angles.
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The arc length is the distance traveled along a circular path as shown in Figure 2 Note that is the radius of curvature of the circular path.
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We define the rotation angle to be the ratio of the arc length to the radius of curvature:
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We can loosely define energy as the ability to do work
Decent "loose" definition
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There is no simple, yet accurate, scientific definition for energy.
In fact, energy is a deep mystery, like entropy and time. There is no standard Joule on display inside a glass case in Paris at the famous Rotonde du Assiette de Crevettes or anything like that. Prof. Richard Feynman taught that energy can be calculated in various ways but he was stumped as to what it is.
It is important to realize that in physics today, we have no knowledge of what energy is. ...there are formulas for calculating some numerical quantity, and when we add it all together it [is] always the same number. [Feynman Lectures]
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The perpendicular lever arm is the shortest distance from the pivot point to the line along which acts;
Good definition.
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Two children push on opposite sides of a door during play.
Good calculation of medium difficulty.
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perpendicular lever arm
This is a vocabulary term, "lever arm."
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the second condition necessary to achieve equilibrium is that the net external torque on a system must be zero.
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newtons times meters
Same as a Joule of energy, rather mysterious!
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Torque is the turning or twisting effectiveness of a force
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When opening a door, you push on it perpendicularly with a force of 55.0 N at a distance of 0.850m from the hinges. What torque are you exerting relative to the hinges?
Basic calculation
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Conservation of Energy
Bypass, although it is interesting. Our main concern, the conservation of total mechanical energy, \(E=GPE+KE\) was developed in a previous section of Ch. 7
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To the mouse and any smaller animal, [gravity] presents practically no dangers. You can drop a mouse down a thousand-yard mine shaft; and, on arriving at the bottom, it gets a slight shock and walks away, provided that the ground is fairly soft. A rat is killed, a man is broken, and a horse splashes. For the resistance presented to movement by the air is proportional to the surface of the moving object. Divide an animal’s length, breadth, and height each by ten; its weight is reduced to a thousandth, but its surface only to a hundredth. So the resistance to falling in the case of the small animal is relatively ten times greater than the driving force.
An object with basic dimension D has surface area proportional to \(D^2\) but mass proportional to \(D^3\). So quadrupling the size, like mouse size to rat size, the area presented to the wind of \(\times 16\) but it has mass \(\times 64\). Mouse is safe but the rat gets greased by higher terminal velocity.
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more generalized fashion as
Good to remember, in a nutshell. We will not use the complicated version involving density, area etc.
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This means a skydiver with a mass of 75 kg achieves a maximum terminal velocity of about 350 km/h while traveling in a pike (head first) position, minimizing the area and his drag. In a spread-eagle position, that terminal velocity may decrease to about 200 km/h as the area increases. This terminal velocity becomes much smaller after the parachute opens.
Discussed 2/13. Of course, the parachute lends an enormous effective area to the skydiver, so that the new terminal speed -- the landing speed -- is slow enough to survive.
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For most large objects such as bicyclists, cars, and baseballs not moving too slowly, the magnitude of the drag force is found to be proportional to the square of the speed of the object.
This is why a concept like terminal velocity arises: the upward drag force depends on the speed, \(\propto v^2\)
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as the person’s velocity increases, the magnitude of the drag force increases until the magnitude of the drag force is equal to the gravitational force, thus producing a net force of zero.
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TAKE-HOME EXPERIMENT
I might actually try this. : )
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Problems & Exercises
No calculations from this section! But plenty of conceptual questions are possible.
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that is, a push or a pull
or the skateboarders' demonstration
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internal forces within the body
e.g., the forces of cohesion that hold the skateboard together, which is why you cannot make a skateboard of jello.
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of all external forces
Note: the net force can be absent from the free body diagram, for clarity, but the net force could also be drawn in over to the side or overlaid on the f.b.d. if labeled clearly and not too cluttered up.
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can be added using the familiar head-to-tail method or by trigonometric methods.
i.e., graphical or analytical methods
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Any force or combination of forces can cause a centripetal or radial acceleration. Just a few examples are the tension in the rope on a tether ball, the force of Earth’s gravity on the Moon, friction between roller skates and a rink floor, a banked roadway’s force on a car, and forces on the tube of a spinning centrifuge
This is an important concept in how we use F = ma. The m and the a are measurable quantities (m) or derived from measurable quantities (a).
The F, however, is a slot that can be filled with tension from a rope or gravitational attraction, electrical repulsion or electrical attraction, a strong nuclear attraction or a week nuclear interaction.
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As a skater forms a circle, what force is responsible for making her turn? Use a free body diagram in your answer
Good free body diagram to work out.
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frictionless banked curve
Frictionless?
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Centripetal force is always perpendicular to the path and pointing to the center of curvature,
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static friction is a responsive force, being able to assume a value less than but no more than
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Linear or tangential acceleration refers to changes in the magnitude of velocity but not its direction. We know from Chapter 6 Uniform Circular Motion and Gravitation that in circular motion centripetal acceleration, refers to changes in the direction of the velocity but not its magnitude.
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At its peak, a tornado is 60.0 m in diameter and carries 500 km/h winds. What is its angular velocity in revolutions per second?
Basic calculation of \(\omega\)
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These equations mean that linear acceleration and angular acceleration are directly proportional.
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Centripetal acceleration ac occurs as the direction of velocity changes; it is perpendicular to the circular motion. Centripetal and tangential acceleration are thus perpendicular to each other.
We discussed this in lecture.
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Explain why centripetal acceleration changes the direction of velocity in circular motion but not its magnitude. 3: In circular motion, a tangential acceleration can change the magnitude of the velocity but not its direction. Explain your answer.
I discussed these two questions at length in lecture
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Analogies exist between rotational and translational physical quantities. Identify the rotational term analogous to each of the following: acceleration, force, mass, work, translational kinetic energy, linear momentum, impulse.
Would make a good matching set. : )
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superposition and interference
Critical for understanding the periodic table, electronegativity, covalent bonding and may more topics in PHY2054 and beyond.
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four types of waves in this picture
Wonderful!
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beating of hearts
IMPORTANT. Electrocardiologists make a "phase space reconstruction" (PSR) of a patient's electrocardiogram,
knowing that a regular sinus rhythm is a very specific oscillatory system, whereas fibrillation, tachycardia etc. are NOT oscillatory. Cf., G.Koulaouzidis, S. Das et al. "Prompt and accurate diagnosis of ventricular arrhythmias with a novel index based on phase space reconstruction of ECG" International Journal of Cardiology, 2015-03-01, Volume 182, Pages 38-43. DOI: 10.1016/j.ijcard.2014.12.067
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Inelastic Collisions in One Dimension
Bypass
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solve
It is interesting to look up various spring constants for springs one can purchase. E.g., this website for Century Springs shows the spring constant as a "rate," in pounds per inch instead of N/m.
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dissipative forces
e.g., friction, aerodynamic drag etc.
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The simplest oscillations occur when the restoring force is directly proportional to displacement.
Concise definition:
- "restoring" \(F=\color{red}-\color{black}kx\)
- "directly proportional to displacement" \(F=-\color{red}kx\)
Good.
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The force constant is related to the rigidity (or stiffness)
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elastic potential energy
I usually call is SPE, spring potential energy, to distinguish from EPE, electrostatic potential energy. But I will try to use EPE in our lectures! : )
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potential energy stored in a spring
Huge concept. It applies from the Big Bang Theory origin of the universe down to the quantum world of electrons and photons and nuclei.
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At a staggering 2.5 million light years from the Earth, this galaxy is the nearest one to our own galaxy
The nearest "proper" galaxy, to be more accurate. The Large and Small Magellanic Clouds are satellite galaxies of the Milky Way, and are less than 250,000 light years away. But they're small and misshapen in comparison to what we typically imagine galaxies to look like.
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A 100-g toy car is propelled
A good brain burner. I will try to do a talking PDF of this one.
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Suppose a 350-g kookaburra
Good basic problem.
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An object’s gravitational potential is due to its position relative to the surroundings within the Earth-object system.
The reason for this is that GPE exists because of an interaction of two bodies: Earth and the other object under consideration
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What is the final speed of the roller coaster
Very similar to Written HW 07 calculation of escape velocity
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this point is arbitrary;
Correct. You can set the zero of any potential energy wherever you like, as long as you stay consistent all the way through your calculations. The reason for this is that work is done when there is a \(\Delta \left(GPE \right)\)
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we refer to this as the
Dr. Brueckner refers to it as GPE
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Because gravitational potential energy depends on relative position, we need a reference level at which to set the potential energy equal to 0.
Note: in the geospatial mini-lecture, the zero of GPE was at infinity.
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boldface symbol, such as , stands for a vector. Its magnitude is represented by the symbol in italics, and its direction by
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this involves determining the perpendicular components of a single vector, for example the x– and y-components,
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Resolving a Vector into Components
Very important
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Applications
Bypass
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The airplane wing is a beautiful example of Bernoulli’s principle in action.
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pressure has units of energy per unit volume, too.
Interesting to think of pressure prepresenting energy independent of bulk motion or position of the center of mass of a pixel of fluid.
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The net work done increases the fluid’s kinetic energy. As a result, the pressure will drop in a rapidly-moving fluid, whether or not the fluid is confined to a tube.
Informal way of stating the Bernoulli principle.
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Compare the kinetic energy of a 20,000-kg truck moving at 110 km/h with that of an 80.0-kg astronaut in orbit moving at 27,500 km/h.
Basic comparison. Good.
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A car’s bumper is designed to withstand a 4.0-km/h (1.1-m/s) collision with an immovable object without damage to the body of the car. The bumper cushions the shock by absorbing the force over a distance. Calculate the magnitude of the average force on a bumper that collapses 0.200 m while bringing a 900-kg car to rest from an initial speed of 1.1 m/s.
A good brain burner. I will make this one into a talking PDF.
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lawn mower.
I detest the lawn mower example. YUKKKK
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How fast must a 3000-kg elephant move to have the same kinetic energy as a 65.0-kg sprinter running at 10.0 m/s?
Another good basic comparison of KE.
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can exert pulls only parallel to its length
and no pushes
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Once you have determined the tension in one location, you have determined the tension at all locations along the rope.
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resolve the tension vectors into their horizontal and vertical components.
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Calculate the tension in the wire
I have used diagrams like this on MANY PHY2053 midterms, frequently with different lengths left and right, so that the dip angles are different. Here the dip angle is 5º left and right, and the ropes form an isosceles triangle. So if I make the ropes different lengths, the angles might be 4º and 8º.
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the acceleration parallel to the incline when there is 45.0 N of opposing friction.
Slightly smaller than without friction. Good, that makes sense
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Extended Topic:
We will bypass this subtopic
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forces parallel to the slope
The force parallel to the slope will exist if there is some tilt angle θ. It equals \(\vec{w}\) if \(\theta=90\) but equals zip zap if \(\theta=0\). So it has to be proportional to the \(\sin\left(\theta\right)\).
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Instead of memorizing these equations, it is helpful to be able to determine them from reason.
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The brake cable on a bicycle carries the tension T from the handlebars to the brake
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general result that if friction on an incline is negligible, then the acceleration down the incline is regardless of mass.
Still, do not memorize this.
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Solving for yields
Modern version of Kepler's third law, although notation is slightly different than I used in lecture.
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they are actually valid for all bodies satisfying the two previously stated conditions.
A short sentence, but powerful.
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2: Calculate the mass of the Sun based on data for Earth’s orbit and compare the value obtained with the Sun’s actual mass.
Good mini-workout
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Examples of gravitational orbits abound.
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find the masses of heavenly bodies
E.g., black holes like Cygnus X-1 and Sagittarius A*, the enormous black hole \(\approx 4\times 10^6 M_{\odot}\) at the center of the Milky Way galaxy.
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Tidal friction exerts torque that is slowing Earth’s rotation
Yes, tidal friction exists, tides due to our moon and to the Sun, but this skips over the main question: can gravity exert a torque on a planet? Take Venus, a planet nearly the size of Earth but no moon to cause significant tidal friction. Answer: no. The gravitational field of the Sun is spherically symmetric, no angular dependence, no vorticity.
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Three children are riding on the edge of a merry-go-round that is 100 kg, has a 1.60-m radius, and is spinning at 20.0 rpm. The children have masses of 22.0, 28.0, and 33.0 kg. If the child who has a mass of 28.0 kg moves to the center of the merry-go-round, what is the new angular velocity in rpm?
Brain burner calculation. I will do a talking PDF for this one.
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The equation is very fundamental and broadly applicable.
target for lecture, 03/22/19
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It seems quite reasonable, then, to define angular momentum as
I do not consider this so reasonable. It is better to say that, in general, for every spatial dimension u, there is a corresponding momentum \(p_u\). In spherical coordinates that could be latitude \(\theta\) and longitude \(\phi\) angles as well as distance from the center of coordinates, \(r\). If the energy states are not dependent on coordinate u, then \(p_u\) is a conserved quantity. For an ice skater, her spin angle can be seen as a longitude angle \(\phi\); he angular momentum, \(p_{\phi}\) is conserved if the ice is smooth enough.
But the author's use of analogy here is OK.
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Conceptual Questions
Notice how many conceptual questions there are? That is significant.
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Calculate the angular momentum of the Earth in its orbit around the Sun.
Planetary angular momentum calculation
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An ice skater is spinning
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Compare this angular momentum with the angular momentum of Earth on its axis.
Spin angular momentum calculation, using the table of moments of inertia.
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These expressions are the law of conservation of angular momentum. Conservation laws are as scarce as they are important.
Our demonstrations with the hand weights and rotating lab stool on Friday were to demonstrate conservation of angular momentum, a huge concept from astrophysics all the way down to quantum mechanics.
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In the next image, her rate of spin increases greatly when she pulls in her arms, decreasing her moment of inertia.
As a student observed, \(I\) and \(\omega\) vary inversely when angular momentum is conserved.
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Suppose a child walks from the outer edge of a rotating merry-go round to the inside. Does the angular veloc
Good conceptual question
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The two-dimensional curved path of the horizontally thrown ball is composed of two independent one-dimensional motions (horizontal and vertical).
Excellent sentence about analysis of a ballistic trajectory
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The two-dimensional curved path of the horizontally thrown ball is composed of two independent one-dimensional motions (horizontal and vertical).
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This is known as "adding in quadrature" -- i.e., add the squares of each perpendicular side.
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adding are perpendicular to each other and thus form a right triangle. This means that we can use the Pythagorean theorem to calculate the magnitude
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there are no additional forces on the ball in the horizontal direction
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Problems & Exercises
You may choose as many of these to practice on as you like.
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Power
Bypass for now.
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A bullet is accelerated down the barrel of a gun by hot gases produced in the combustion of gun powder. What is the average force exerted on a 0.0300-kg bullet to accelerate it to a speed of 600 m/s in a time of 2.00 ms (milliseconds)?
Basic impulse calculation
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The quantity is given the name impulse.
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Example 1:
Skip this example. It is basically a trig workout
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the force (to bring the occupant to a stop) will be much less if it acts over a larger time.
Perfect description
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average effective force
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chickens
Forget about the chicken
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A system is said to be in stable equilibrium if, when displaced from equilibrium, it experiences a net force or torque in a direction opposite to the direction of the displacement.
Very important. Most machines have vibrations about an equilibrium configuration, like a car that is traveling really fast on the turnpike, so fast that the car starts to shake.
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some systems in stable equilibrium are more stable than others.
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unless some effort is made to keep it moving.
This was Aristotle's view. An arrow flies through the air because it presses into the air, air rushes bacwards behind the arrow and then pushes the arrow forward.
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Extrapolating to a frictionless surface
an extrapolation that Galileo first made.
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graphically, using the head-to-tail method, or analytically, using components. The techniques are the same as for the addition of other vectors, and are covered in Chapter 3 Two-Dimensional Kinematics.)
Why we concentrated on that part of Ch. 3
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we assume the vertical forces cancel
This is not unreasonable. The normal force, perpendicular to the surface, i.e., to the rails, rises from the intermolecular and interatomic forces in the steel alloy of the rails. They act like little trampolines, dipping just enough to support whatever weight is on it... up until the weight passes the rail's breaking point.
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For completeness, the vertical forces are also shown; they are assumed to cancel since there is no acceleration in the vertical direction. The vertical forces are the weight and the support of the ground
As in HW 3.
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It can help us make predictions.
HUGE
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The energy moves forward through the water, but the water stays in one place.
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The waves on the strings of musical instruments are transverse
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For earthquakes, there are several types of disturbances, including disturbance of Earth’s surface and pressure disturbances under the surface.
Another seismic wave phenomenon is a seiche
Cf., What is a seiche?
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For earthquakes, there are several types of disturbances, including disturbance of Earth’s surface and pressure disturbances under the surface.
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Sound waves in air and water are longitudinal.
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and energy
Also momentum. Because electromagnetic radiation propagates momentum and energy across spacetime, we have an opportunity to harness sunlight in outer space and use it in a solar sail, to navigate here and there in the solar system.
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Laminar flow is characterized by the smooth flow of the fluid in layers that do not mix. Turbulent flow, or turbulence, is characterized by eddies and swirls that mix layers of fluid together.
Good comparison of idealized laminar flow with turbulent flow. Planes spew wake turbulence, very dangerous for following aircraft.
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objects are larger than the size of most molecules
I.e., non-quantum
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much, much less than the speed of light
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his ideas were eventually accepted by the church and scientific communities.
A short paragraph to describe a very complex controversy! The paragraph is acceptable, but does not do it justice. Well worth reading about, e.g., Galileo's Daughter, by Dava Sobel (UCF Main Library General Collection - 4th Floor QB36.G2 S65 1999 Available)
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Forces and Torques in Muscles and Joints
Bypass until you are ready to take MCAT or are already in med school, PT school etc.
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The displacement as a function of time t in any simple harmonic motion
We discussed this in Lecture 32
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PERIOD OF SIMPLE HARMONIC OSCILLATOR
We worked on this in Lecture 33.
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5.3 Elasticity: Stress and Strain
Bypass this entire section
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Momentum, like energy, is important because it is conserved.
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This equation means that the total kinetic and potential energy is constant for any process involving only conservative forces.
Conservation of total mechanical energy $$E = GPE+KE$$ which we used on Written HW 07.
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Potential Energy of a Spring
Bypass until after Exam 3.
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Nonconservative Forces
Bypass
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Work, Energy, and Power in Humans
Bypass
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work done on a system by a constant force is defined to be the product of the component of the force in the direction of motion times the distance through which the force acts.
$$F_{||} \Delta s$$
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Rotational Kinetic Energy
Very cool topic to complete the rotational analogies, but I will reserve this for after Exam 3.
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10.4
Ready to work on this topic starting 03/27
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6.4 Fictitious Forces and Non-inertial Frames: The Coriolis Force
We will bypass this section, but it is interesting to read about Coriolis force in regard to hurricanes and weather systems. Cf., Fig. 5
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This is the ordinary assumption in elementary physics. Air flow properties are very difficult to model, so we ignore them. This is the same as saying to our speeds are not large enough to draw appreciable drag from the air, so they can be ignored... until you need high precision!
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World Energy Use
Bypass
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First, the equation for conservation of momentum for two objects in a one-dimensional collision is
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Kinematics of Rotational Motion
Not a total bypass but we did not talk too much about this information in lecture.
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four rotational kinematic equations (presented together with their translational counterparts):
nice
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In physics, the definition of time is simple
Oh, no! Nothing could be further from the truth! But we can provisionally accept this statement for the moment.
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Collisions of Point Masses in Two Dimensions
Bypass until after Exam 3
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Introduction to Rocket Propulsion
We have talked about rocket motors and their effects, but consider this section is a bypass.
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