Part a: A newly discovered planet has a mean radius of 4030 km. A vehicle on the planet's surface is moving in the same direction as the planet's rotation, and its speedometer reads 169 km/h. If the angular velocity of the vehicle about the planet's center is 5.28 times as large as the angular velocity of the planet, what is the period of the planet's rotation?
b: 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?
ω = (tangential v)/R
T = 2∏/(ω)
The Attempt at a Solution
I have found that the angular velocity of the car is .0397 rad/h, and the angular velocity of the planet is .0075 rad/h (please confirm whether these values are correct!). For part a, what should I plug in as my ω to find the period of the planet's rotation? For part b, how do I set it up to find tangential v?