Angular momentum of disk & clay?

In summary, the problem involves a rotating disk and a falling clay ball that sticks to the edge of the disk. The angular momentum of the combined system just before impact is calculated by adding the angular momenta of the disk and the clay ball, taking into account their respective masses, velocities, and distances from the center of rotation. The direction of the angular momenta must be considered as well, as it is a vector quantity.
  • #1
Kibbel
27
0

Homework Statement



A rotating uniform-density disk of radius 0.7 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 0.4 kg falls and sticks to the outer edge of the wheel at location A, < -0.42, 0.560, 0 > m. Just before the impact the clay has a speed 6 m/s, and the disk is rotating clockwise with angular speed 0.34 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.)

Homework Equations


moment of inertia for a disk is (mr^2)/2
Angular momentum = Iw
Angular momentum = R(perpendicular)*momentum*w

The Attempt at a Solution


okay so its l split it into two angular momenta, of the clay, and of the wheel and added them together

wheel 1/2*m*(r^(2))*w + R(perpendicular)*momentum of clay

momentum of clay = mass * velocity of clay

so I got .5*(3.6)*(.7^2)*<0,0,-0.34> + 0.42*(6*.4)*<0,0,1>

is this right? i think it is, but I am not sure if that's set up correctly..
 
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  • #2
You mention the speed of the clay, but you say nothing about its velocity. In what direction is the clay moving just before impact?
 
  • #3
its moving in the negative y, does that matter?
 
  • #4
Yes it matters. If the velocity of the clay is parallel to the axis of rotation, then you need not worry about its initial angular momentum; if it is not, you do. "Negative y" means nothing to me without a picture. Can you provide one?
 
  • #6
You need to be careful about the sign of the initial angular momentum of each component. Are the two initial angular momenta in the same or in opposite directions?
 
  • #7
the disk is spinning clockwise so its in the -z,

and the right hand rule states that the balls momenta is in the +z?

So i have

((mr^2)/2)w + Rperpendicular(Mass*Velocity)w

=

((3.6kg)*(.7m)^2)/2 * <0,0,-.34> + (0.42m)(0.4kg*-6m/s)*<0,0,1>
 
  • #8
im not sure the direction of the momentum matters, because with R perpendicular its multiplied by the magnitude of P
 
  • #9
Angular momentum is a vector. For a particle

[tex]\vec{L}=m\vec{r}\times \vec{v}[/tex]

and for a rigid body

[tex]\vec{L}=I \vec{\omega}[/tex]

You need to add the angular momenta as vectors.
 
  • #10
thank you man, i was doing the IW for the rotation for the disk,

and the equation i had with the r perpendicular and momentum included direction because of the right hand rule of the ball i think
 
  • #11
So can you answer the question now?
 
  • #12
yea thankyou
 

1. What is angular momentum?

Angular momentum refers to the rotational motion of an object around a fixed point or axis. It is a measure of the amount of rotational energy an object possesses.

2. How is angular momentum of a disk calculated?

The angular momentum of a disk is calculated by multiplying the mass of the disk by its rotational velocity and its distance from the axis of rotation.

3. What factors affect the angular momentum of a clay object?

The angular momentum of a clay object is affected by its mass, rotational velocity, and distance from the axis of rotation. It can also be affected by external forces such as friction or air resistance.

4. How does the angular momentum change when a disk or clay object is rotating?

The angular momentum of a rotating disk or clay object remains constant unless acted upon by an external torque. This is known as the law of conservation of angular momentum.

5. Can angular momentum be transferred between objects?

Yes, angular momentum can be transferred between objects through collisions or interactions. In an isolated system, the total angular momentum will remain constant, but it may be redistributed among the objects involved.

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