"In classical physics," Bengt thinks, "momentum is always mass times velocity, m * v. In relativistic physics, momentum is usually taken to be m * v / gamma. But if you really want, you can decide that it is m * v after all, and use speed-dependent mass. And since the earth is moving, it gets a higher mass."
- Assuming that the earth is spinning, but that its centre of mass is at rest, how much does its relativistic mass increase compared to if it was standing still?
- If the earth is also spinning around the sun, how much does that increase its mass?
- Bengt's (rest) mass is 100 kg. If the mass of the earth increases, gravity should get stronger. Also, Bengt moves along with the earth, so his mass should increase too. If Bengt is at the equator, and the earth moves as in b), how much weight does he gain?
- The rotation of the earth also leads to a centrifugal force, so that Bengt seems to get lighter instead. If Bengt is at the equator, how much is his apparent weight loss?
- The rotation of the earth has some other consequences. Normally, the circumference of a circle (or a sphere, in this case) is pi * D, where D is the diameter. But if you try to measure the equator, it is because of length contraction not quite pi * D. But again, if you really want, you can decide that it is pi * D after all, and use speed-dependent pi. In that case, how much does pi change when you measure the equator?
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