How Does Impact Affect System Angular Momentum?

[fball558]

system angular momentum??

Homework Statement

A rotating uniform-density disk of radius 0.9 m is mounted in the vertical plane. The axle is held up by supports that are not shown, and the disk is free to rotate on the nearly frictionless axle. The disk has mass 3.6 kg. A lump of clay with mass 0.6 kg falls and sticks to the outer edge of the wheel at the location < -0.585, 0.684, 0 > m. Just before the impact the clay has a speed 9 m/s, and the disk is rotating clockwise with angular speed 0.65 radians/s.


(a) Just before the impact, what is the angular momentum of the combined system of wheel 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.)


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

The Attempt at a Solution

I said clay ball has momentum only in the y direction. it is falling at 9 m/s and has mass .6 kg so .6 * 9 = 5.4 since it is falling i believe this would be negative.
now I am stuck on the disk. how do i find the x and y component??

 

[fball558]

for the disk would the z component be found by
L = wI where L is angular momentum??
i do this and get 28.187
does this sound right??

 

[nlightner]

I would like to clarify and provide a more complete explanation of the concept of system angular momentum.

System angular momentum is a physical quantity that describes the rotational motion of a system. It is defined as the product of the moment of inertia and the angular velocity of the system. In simpler terms, it is a measure of how much rotational motion a system has and how fast it is rotating.

In this problem, the system consists of the rotating disk and the falling clay ball. Just before the impact, the system has a certain angular momentum, which is the sum of the individual angular momenta of the disk and the clay ball. The angular momentum of the disk can be calculated using the formula L = Iω, where I is the moment of inertia and ω is the angular velocity. The moment of inertia of a uniform-density disk rotating about its central axis is given by I = 1/2MR^2, where M is the mass of the disk and R is the radius. Therefore, the angular momentum of the disk before the impact is L = (1/2)(3.6 kg)(0.9 m)^2(0.65 rad/s) = 1.404 kg·m^2/s.

For the clay ball, its angular momentum can also be calculated using the same formula, L = Iω, where I is the moment of inertia and ω is the angular velocity. However, since the clay ball is falling vertically, its angular velocity is zero. Therefore, its angular momentum is also zero.

To find the x and y components of the angular momentum, we can use vector addition. The x component of the angular momentum is zero for both the disk and the clay ball, since their velocities are in the y direction. Therefore, the total x component of the angular momentum is also zero.

The y component of the angular momentum can be calculated by taking into account the direction of rotation. The disk is rotating clockwise, so its y component will be negative. The clay ball is falling downwards, so its y component will also be negative. Therefore, the total y component of the angular momentum is (-1.404 - 5.4) kg·m^2/s = -6.804 kg·m^2/s.

After the impact, the clay ball sticks to the outer edge of the wheel, so the system now consists of a rotating disk with a lump of clay attached to it