Motion and Relativity

What the course covers

Classical mechanics is three laws and a catalogue of forces, and almost everything else in the first half of this course is those laws integrated once or twice: work and energy, momentum and collisions, torque and angular momentum, gravitation, and the harmonic oscillator that every stable system becomes when you nudge it gently. Then it breaks. Maxwell predicts a light speed with no frame attached, Michelson and Morley cannot find the ether, and fast electrons refuse to obey $K = \frac{1}{2}mv^2$. Einstein keeps the principle of relativity and the constancy of $c$ and throws away absolute time, and out come dilation, contraction, the collapse of simultaneity, $\overrightharpoon{p} = \gamma m\overrightharpoon{v}$ and $E = \gamma mc^2$. It ends where the equality of inertial and gravitational mass leads: gravity as the shape of spacetime.

The laws of motion

1. What a frame really is. There is no such place as still.
2. The first law. A definition wearing a law’s clothing.
3. Force changes momentum. Why it is not really $F = ma$.
4. The third law. Find the other half of the pair.
5. Where momentum conservation comes from. Two laws in, a conservation law out.
6. Mass, weight and the kilogram. One is yours, one is your address.
7. The four fundamental forces. Everything, from only four.
8. Contact forces. Nothing ever really touches.
9. Friction and drag. The forces that read your velocity.
10. From force to trajectory. Integrate twice and you are done.
11. Projectile motion. Two motions that ignore each other.
12. Range, height and the best angle. Where forty-five degrees comes from.
13. The laws of motion review. Three laws and everything under them.

Work, energy and power

14. Work is force along the path. Only the useful component counts.
15. When the force keeps changing. Chop the path, add the pieces.
16. Power. Not how much, but how fast.
17. The work-energy theorem. Where one-half m v squared is hiding.
18. Conservative forces. Some forces give it back.
19. Potential energy. Work put into storage.
20. Two potential energies you will never stop using. The recipe, run twice.
21. Conservation of mechanical energy. A number that refuses to change.
22. Reading a potential energy landscape. The graph is the physics.
23. Work and energy review. One integral, and everything after it.

Momentum and collisions

24. Impulse. When you cannot use suvat.
25. Why momentum survives a collision. Gravity does not get a turn.
26. Elastic, inelastic and sticky. One question sorts them all.
27. Solving an elastic collision. The relative velocity simply reverses.
28. Choosing a neutron moderator. Why reactors use water, not lead.
29. The centre of mass. One point that behaves itself.
30. The centre of mass frame. Sit on the point and watch.
31. Collisions in two dimensions. Momentum is really three laws.
32. Momentum and collisions review. What survives, and what does not.

Rotation

33. Circular motion. Turning is accelerating.
34. Angular momentum. Momentum, with a lever arm.
35. Torque. The second law, rotated.
36. Moment of inertia. Mass cares where it sits.
37. Conservation of angular momentum. Pull your arms in, spin faster.
38. Rotation review. The same laws, one dictionary later.

Gravitation

39. Newton’s law of gravitation. The apple and the Moon, one law.
40. Gravity from many masses. Add the pulls, one by one.
41. Why a planet acts like a point. Newton’s hardest theorem.
42. Gravity is a central force. No torque, so no change.
43. Equal areas in equal times. Kepler’s law, in three lines.
44. Weighing the Earth. Read the formula backwards.
45. Gravitational potential energy. Why the answer is negative.
46. Escape speed. Fast enough to never come back.
47. Gravitation review. One force, from apples to galaxies.

Oscillations

48. Why almost everything oscillates. Every valley is a parabola close up.
49. The defining equation. Acceleration that points home.
50. The solution. Amplitude, frequency, phase.
51. Velocity and acceleration. Three waves, a quarter cycle apart.
52. The vertical spring. Gravity only moves the zero.
53. The simple pendulum. Harmonic, but only if you are gentle.
54. Energy in oscillation. Half and half, on average.
55. Damping. Under, critical, over.
56. How the energy leaks away. Amplitude halves, energy quarters.
57. Oscillations review. One equation, all of nature.

The road to relativity

58. Galilean relativity. The transformation Newton assumed.
59. Why Newton survives a boost. Speeds add, accelerations do not change.
60. A speed with no frame attached. Maxwell’s inconvenient constant.
61. The ether. A substance that could not exist.
62. Michelson and Morley. Looking for a wind that was not there.
63. What the null results proved. It takes three experiments, not one.
64. Fast electrons break Newton. Mechanics fails before light does.
65. Einstein’s two postulates. Keep both pillars, drop the floor.
66. The road to relativity review. Three pillars, one had to fall.

Time, space and Lorentz

67. The light clock. Moving clocks run slow, and here is why.
68. The gamma factor. Why you never noticed.
69. Proper time. Name the clock that is not confused.
70. Length contraction. Distance shrinks along the motion.
71. Proper length. Measuring a moving rod is about clocks.
72. Deriving the Lorentz transformations. Four assumptions, one answer.
73. The master equations. Everything, from four lines.
74. The relativity of simultaneity. At once is not a property of events.
75. The train and the platform. Both are shorter. Both are right.
76. The twin paradox. One of them turns around.
77. Muons from the sky. The experiment that settles it.
78. Time and space review. One transformation, all of it.

Relativistic kinematics

79. Adding velocities. Three quarters plus three quarters is not one and a half.
80. The speed limit. Feed it light and light comes out.
81. The spacetime interval. The one thing everybody agrees on.
82. The classical Doppler effect. A medium can tell who is moving.
83. The relativistic Doppler effect. Only the relative speed can appear.
84. Reading the sky. One line, and you have the speed.
85. Relativistic kinematics review. What adds, what is fixed, what shifts.

Relativistic mechanics

86. Newtonian momentum breaks. A conservation law that stops working.
87. Relativistic momentum. One gamma puts it right.
88. Relativistic mass, and why it was retired. A phrase to understand, then drop.
89. The second law, relativistically. Now you see why it was never $F = ma$.
90. Relativistic kinetic energy. Do the work integral again.
91. Checking the low-speed limit. Newton, hiding in the first term.
92. Rest energy. The term that survives standing still.
93. Mass is energy. The Sun weighs less every second.
94. Binding energy. A helium nucleus weighs too little.
95. Electronvolts. Units built for the job.
96. The energy-momentum invariant. The same number in every frame.
97. Massless particles. How light carries momentum.
98. Solving a decay. Conserve, conserve, invariant.
99. Relativistic mechanics review. Mass, energy and momentum as one.

General relativity

100. The equivalence principle. Einstein’s happiest thought.
101. Gravity is geometry. Straight lines in a bent space.
102. Mercury’s missing arcseconds. A discrepancy nobody could explain.
103. Light bends. The eclipse that made Einstein famous.
104. Clocks in a gravitational well. Time runs slow near mass.
105. GPS. Relativity, in your pocket.
106. Gravitational waves. Ripples in the shape of space.
107. What LIGO heard. Three suns, into pure geometry.
108. General relativity review. Where the course points next.

One lesson in full

The spacetime interval. The one thing everybody agrees on.

A question to try

All university physics courses