Angular Momentum before and after being hit with a ball of clay

1. Nov 16, 2009

Qnslaught

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

A device consists of eight balls each of mass 0.7 kg attached to the ends of low-mass spokes of length 1.8 m, so the radius of rotation of the balls is 0.9 m. The device is mounted in the vertical plane. The axle is held up by supports that are not shown, and the wheel is free to rotate on the nearly frictionless axle. A lump of clay with mass 0.23 kg falls and sticks to one of the balls at the location shown, when the spoke attached to that ball is at 45 degrees to the horizontal. Just before the impact the clay has a speed 6 m/s, and the wheel is rotating counterclockwise with angular speed 0.10 radians/s.

(a) Which of the following statements are true about the device and the clay, for angular momentum relative to the axle of the device?

The angular momentum of the falling clay is zero because the clay is moving in a straight line.

The angular momentum of the device is the same before and after the collision.

The angular momentum of the device + clay just after the collision is equal to the angular momentum of the device + clay just before the collision.

The angular momentum of the device is the sum of the angular momenta of all eight balls.

Just before the collision the angular momentum of the wheel is 0.

2. Relevant equations

3. The attempt at a solution

I'm pretty sure the clay has angular momentum, so I think the first one is right. I'm not sure about the second one but I don't think it's right. I think the angular momentum of the system stays the same. I think the momentum of the device is the sum of all the balls. And I don't think the angular momentum of the wheel is 0.

2. Nov 16, 2009

kuruman

Angular momentum (like torque) needs a reference point. The problem gives none. However, let us assume that the angular momentum is referred to the axis of the wheel. How do you find the angular momentum of a moving point mass with respect to some reference point?

3. Nov 16, 2009

Qnslaught

Well if I used that as a reference point then, the clay falling would have an angular momentum right?

4. Nov 17, 2009

kuruman

To answer question 1 you need to know how to calculate the angular momentum of the clay relative to the wheel's axis. If you do the calculation and the answer is zero, then the clay has no angular momentum. If you do the calculation and the answer is not zero then the clay does have angular momentum.

What is the definition of angular momentum for a point mass?