# Angular momentum of a multicomponent system

## Homework Statement

A device consists of eight balls each of mass 0.4 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 0.10 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 5 m/s, and the wheel is rotating counterclockwise with angular speed 0.07 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 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.
The angular momentum of the falling clay is zero because the clay is moving in a straight line.
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.

(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,i = < , , > kg · m2/s

(c) Just after the impact, what is the angular momentum of the combined system of device plus clay about the center C?
C,f = < , , > kg · m2/s

(d) Just after the impact, what is the angular velocity of the device?
f = < , , > radians/s

(e) Qualitatively, what happens to the total linear momentum of the combined system? Why?
There is no change because linear momentum is always conserved.
Some of the linear momentum is changed into angular momentum.
Some of the linear momentum is changed into energy.
The downward linear momentum decreases because the axle exerts an upward force.

(f) Qualitatively, what happens to the total kinetic energy of the combined system? Why?
Some of the kinetic energy is changed into angular momentum.
The total kinetic energy decreases because there is an increase of thermal energy in this inelastic collision.
Some of the kinetic energy is changed into linear momentum.
There is no change because kinetic energy is always conserved.

## Homework Equations

L(device)=8*(I x omega); 8 because there are 8 balls
I=MR^2
omega in this case is 0.07 radians
L(clay)=R*cos(45)*mv

## The Attempt at a Solution

So I know for parts b, c and d that all of the x and y components are 0. I attempted to solve for L(C,i) by adding together both of the equations I have above, and I get 0.500 kg*m^2/s, which is incorrect. Can somebody please let me know what I am doing wrong with the equation?

i am working on this problem as well all i have is the 0's and for letter (f)
it is the total kinetic energy dcreases because there is an increase of thermal energy.
stuck on the rest.

I think the moment inertia for a ball is (2/5MR^2), however I don't know what else goes into computing the angular momentum. I am working on this same hw problem and only have b, c, and d left to do.

hey hatinengr,
did you get problem #2
how do you find the P of the sat?
and what you get for the multiple choice question (not the one dealing with direction)

Multiply out the velocities and masses given and add them for Pinitial. Find final p of junk and subtract it from intitial sum.

for the mc, its the 3 choices that say that things stay the same at loc. a,b, and c.

I really need help with the original problem though. I have tried to find the sum of the eight angular momenta of the balls and subtracted that of the lump of clay since it is moving in the negative z direction. i am getting it wrong though.

the problem is that the picture is misleading. there are really only 2 balls, and the picture shows those two balls at 4 different periods in time. You should get the right answer now.

woops sorry wrong problem

i finally got this problem. moment of inertia of the device is 8*(MR^2). You subtract sin(45)Rmv from it to get angular momentum. The problem has expired now so unfortunately it may not help.