Suppose the moon were held in its orbit not by gravity but by the tension in a massless cable. You are given that the period of the moon's orbit is T = 27.3 days, the mean distance from the earth to the moon is R = 3.85 x 108 m, and the mass of the moon is M = 7.35 x 1022 kg.

What would the tension in the cable be?

HELP: Remember that the moon is going around the earth in a circle. Therefore, there is centripetal acceleration. What is this acceleration?
HELP: Newton's 2nd Law says that if there is an acceleration, then there must be a force. What is the force required to provide the centripetal acceleration?


So, I think I should be using T=m*acceleration, acceleration=w^2*Radius where w=angular velocity, and w=2pf, but I don't know how to get w.

You're on the right track. By "w" I assume you mean rotational velocity, usually shown as omega, ω. You can calculate ω if you know the period, T:

ω = 2π/T

To get the units all into proper SI form you will need to convert the period of 27.3 days to seconds, so that you get ω in units of . Then the tension can be calculated as you propose: