A newly discovered planet has a mean radius of 5370 km. A vehicle on the planet\

Question

A newly discovered planet has a mean radius of 5370 km. A vehicle on the planet's surface is moving in the same direction as the planet's rotation, and its speedometer reads 121 km/h. If the angular velocity of the vehicle about the planet's center is 2.28 times as large as the angular velocity of the planet, what is the period of the planet's rotation?

If the vehicle reverses direction, how fast must it travel (as measured by the speedometer) to have an angular velocity that is equal and opposite to the planet's?

Explanation / Answer

v = 121000 / 3600 = 33.6 m/s   for speed of vehicle

Let wp be angular speed of planet and wv the angular speed of vehicle

V = wp R + v     where V is speed of vehicle relative to center of planet

Since V = wv R   we have

wv - wp = v / R

2.28 wp - wp = v / R

wp = 33.6 / (1.28 * 5.37 * 10E6) = 4.89 * 10E-6 / sec    angular velocity of planet

Part II

wv must be 4.89 * 10E-6 in the opposite direction

v = wv * R = 4.89 * 10E-6 * 5.37 * 10E6 = 26.3 m/s

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