# Central Force Motion

1. Jul 13, 2013

### postfan

1. The problem statement, all variables and given/known data
An object of mass M moves under the influence of an attractive central force F = - A r^4 \hat{r} where \hat{r} is a unit vector in the radial direction.
If the object is in a circular orbit of radius R , find its speed v as a function of M,A, and,R.

2. Relevant equations

a=v^2/r

3. The attempt at a solution

I rearranged the above equation to v=sqrt(ar). I know that the radius is R but I dont know what the acceleration is. Help!

2. Jul 13, 2013

### rude man

What is the force necessary to keep a mass M in circular motion with radius R?

Equate this force with the given force.

3. Jul 13, 2013

### postfan

I don't understand what you are saying.

4. Jul 14, 2013

### jhosamelly

You need to think about the centripetal force.

$F=\frac{mv^2}{r}$

That is the force needed to keep an object in circular motion. Equate this with your central force.

Last edited: Jul 14, 2013
5. Jul 14, 2013

### D H

Staff Emeritus
You also know the constant A, the radius R, and the mass M. So what's the acceleration?

6. Jul 14, 2013

### postfan

I still don't understand. Could you please give me a hint?

7. Jul 14, 2013

### D H

Staff Emeritus
F=ma. Divide the force by the mass.