How Does Adding Mass Affect the Angular Momentum of a Rotating System?

[luckylauren]

A device consists of eight balls each of mass 0.8 kg attached to the ends of low-mass spokes of length 1.2 m, so the radius of rotation of the balls is 0.6 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 0.20 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 9 m/s, and the wheel is rotating counterclockwise with angular speed 0.28 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?

Just before the collision the angular momentum of the wheel is 0.
The angular momentum of the device is the same before and after the collision.
The angular momentum of the device is the sum of the angular momenta of all eight balls.
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 falling clay is zero because the clay is moving in a straight line.



(b) Just before the impact, what is the angular momentum of the combined system of device plus clay about the center C? (As usual, x is to the right, y is up, and z is out of the screen, toward you.)


(c) Just after the impact, what is the angular momentum of the combined system of device plus clay about the center C?

(d) Just after the impact, what is the angular velocity of the device?




i understand the purpose of using the equation for L but not for this case =[

 

[LowlyPion]

See:
https://www.physicsforums.com/showthread.php?t=305456

 

[nlightner]

a) 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 device is the same before and after the collision.
- The angular momentum of the device is the sum of the angular momenta of all eight balls.
- 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.

b) Just before the impact, the angular momentum of the combined system of device plus clay about the center C is zero. This is because the system is not rotating about the center C at this point and the angular momentum is defined as the product of the moment of inertia and angular velocity.

c) Just after the impact, the angular momentum of the combined system of device plus clay about the center C is not zero. This is because the clay has now become a part of the system and is rotating along with the device.

d) Just after the impact, the angular velocity of the device can be calculated using the conservation of angular momentum. The moment of inertia of the system has increased due to the addition of the clay, but the angular momentum must remain the same. Therefore, the angular velocity of the device will decrease to compensate for the increase in moment of inertia. The exact value of the angular velocity can be calculated using the equation L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.