# Uniform Circular Motion of an object

1. Nov 19, 2007

1. The problem statement, all variables and given/known data
A horizontal force of 210N is exerted on a 2.0kg object as it rotates uniformly on a horizontal plane with a radius of 0.9m. Calculate the speed of the object.

2. Relevant equations
I THINK the relevant equations for this problem are v=2$$\Pi$$r/T and ar=v^2/r.

3. The attempt at a solution
v=2$$\pi$$0.9/???
ar=???/0.9

My biggest problem is that for the life of me, I can't figure out how to find either the T or the v. If I knew how to do that, I could figure out the problem. I've also drawn a diagram of the problem.

2. Nov 19, 2007

### Galileo's Ghost

You won't need to find T. Use your equation for "ar" as you suggest, but remember Newton's Second Law... F = ma. Since you know the Force, v can be calculated. No T needed, but if you are curious, T can be calculated now that you know v!!!

3. Nov 19, 2007

### PhanthomJay

All you need to know is that the radial acceleration (or centripetal acceleration ) is v^2/r, as you have noted. Then use newton's 2nd law in the radial (centripetal) direction to calculate v, the tangential speed .

4. Nov 19, 2007

In this case, would my F=m(a) be 2.0(210)?

I'm thinking I need to find "a" first... perhaps a=Fnet/m?

Last edited: Nov 19, 2007
5. Nov 19, 2007

### Galileo's Ghost

No...F = 210, m = 2.0, a is given by the equation you have stated...v^2/r

6. Nov 20, 2007

Hmmm...

F=ma and a=v^2/r... F=m(v^2/r)

v^2/r=F/m

v^2=Fr/m

v=sqrtFr/m

v=sqrt 210(.9)/2.0

v= 9.7 m/s^2

7. Nov 20, 2007

### azatkgz

Right!!

8. Nov 20, 2007