A newly discovered planet has a mean radius of 1350 km. A vehicle on the planet\

Question

A newly discovered planet has a mean radius of 1350 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 8.28 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

speedometre will read the actual velocity of the plain = 121 km/hr = 33.6m/s

angular velocity = 33.6/1350*10^3 = 2.48 *10^-5

angular velocity of the planet = 2.48*10^-5/8.28 = 2.99*10^-6

time = 2*pi/angular velocity = 252321.4286*8.28 sec = 580.33 hrs

to have planet 's angular velocity ie 2.99*10^-6 = 2.99*10^-6 *1350*10^3 = 4.04 m/s

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