# Rotational inertia

1. Oct 4, 2007

### Oblio

A cockroach of mass m runs counterclockwise around the rim of a lazy Susan (a circular disc mounted on a vertical axle) of radius R and rotational inertia I with frictionless bearings. The cockroach's speed relative to the earth is v, where as the lazy Susan turns clockwise with angular speed wo. The cockroach finds a bread crumb on the rim and, or course stops. a) what is the angular speed of the lazy susan after cockroach stops. b.) Is mechanical energy conserved?

I'm not sure how to relate the cockroach's linear speed with the angular speed of the disc......

I'd love any help..
thanks!

2. Oct 5, 2007

### learningphysics

Use conservation of angular momentum... take clockwise positive... counterclockwise negative... what is the angular momentum of the cockroach before it stops... what is the angular momentum of the lazy Susan before the cockroach stops?

angular momentum afterwards the roach stops equals angular momentum before...

3. Oct 5, 2007

### andrevdh

Try and use conservation of angular momentum - assume that the LS has none when the cc gets on it.

4. Oct 5, 2007

### Oblio

How do I manage to use a linear speed of (cockroach) when its spinning though? isnt rotational motion acceleration?

It doesnt make sense to me...

5. Oct 5, 2007

### Staff: Mentor

The cockroach has both linear momentum and angular momentum. Given the first and the distance from the axis, you can calculate the second. (Treat the cockroach as a point mass.)

6. Feb 14, 2008

### keltix

w= ( mRv - Iwo ) / ( I + mR^2 )