# Rotational kinematics on a plane

1. Apr 6, 2009

### dherm56

1. The problem statement, all variables and given/known data

A circular hoop rolls down a ramp without slipping. The angle of the ramp with respect to horizontal is 30 degrees.

1) What is the acceleration of the center of mass of the hoop down the ramp?

a = ( 1/4 ) g
a = ( 1/3 ) g
a = ( 1/2 ) g
a = ( 2/3 ) g
a = ( 3/4 ) g
2. Relevant equations

rotational kinematics with potential and kinetic energy

3. The attempt at a solution

a=gsin30
a=.5g

I'm not sure if there is more to the problem, any suggestions

2. Apr 6, 2009

### AEM

You should set up your coordinate system as usual (x axis along the plane; y axis perpendicular). Then write a set of translational equations based on F = ma and a set of rotational equations based on

$$\tau = I \alpha$$

You'll need the moment of inertia for the hoop and to recall that $$\alpha = \frac{a}{r}$$. While you're considering the rotational motion, keep in mind that the force of friction caused the hoop to rotate. With all these pieces you should be able to arrive at the answer.

3. Apr 6, 2009

### rl.bhat

Write down the expression for net force and torque on sliding hoop and solve for a(cm)