Question kinetic energy in circular motion

Homework Statement

An object moves in uniform circular motion. Its kinetic energy is directly proportional to:
I. centripetal force
III. the period of circular motion

Homework Equations

I took the universal gravitational law

G* m1 * m2 /r^2 = m2 * v^2/r

and then I rearranged for the kinetic energy of circular motion to get:

G * m1 * m2 /r = m2 * v^2 /2

The Attempt at a Solution

Looking at my equation, I was able to see that the bigger the centripetal force is, the more kinetic energy we have. I is an option.

As the radius gets bigger, the kinetic energy decreases, so II is out.

As the period of circular motion gets bigger, the velocity decreases, to the kinetic energy is not directly proportional.

Thus, I chose only I. However, the solutions say that the answer is I and II.

Why is this the case? Thanks a lot in advance!

gneill
Mentor
The question does not mention gravity or orbits, just circular motion. You should work with expressions that apply generally to objects in circular motion.

Start by writing expressions for KE, Fc (Centripetal force) , and T (period) in terms of v and r.

Never mind. I got it.

Fc = m*v^2/r.

rFc/2 = 0.5 * m * v^2 = K.E.

I see it now. Thanks so much!