Physics · Mathematical methods and mechanics. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
Rotation copies linear motion. Torque takes the place of force, moment of inertia I takes the place of mass and angular momentum L = Iω takes the place of momentum. I depends on how far the mass lies from the axis, so the same body has different values of I about different axes. If no external torque acts, L stays constant.
Gravitation is an inverse-square attraction between masses, with distances measured between centres. In a circular orbit gravity supplies the centripetal force, which fixes the orbital speed and period at each radius.
Kepler's laws follow from this: orbits are ellipses, the line to the Sun sweeps equal areas in equal times, and T2 ∝ r3.
Measuring distance from the surface instead of from the centre. At a height equal to the Earth's radius, r = 2R, so g falls to one quarter, not one half.
Answer: 3 rad s−1.
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