Angular momentum multiparticle system

In summary, the conversation discusses a rotating uniform-density disk with a mass of 3.6 kg and a lump of clay with a mass of 0.4 kg that falls and sticks to the outer edge of the disk. The angular momentum of the combined system is discussed before and after the impact, and the moment of inertia of a disk is mentioned. The direction of the angular momentum is determined to be negative y due to the clay falling on the disk. The momentum is conserved throughout the discussion.
  • #1
solrac214
7
0
1. 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 0.4 kg falls and sticks to the outer edge of the wheel at the location < -0.81, 0.392, 0 > m. Just before the impact the clay has a speed 9 m/s, and the disk is rotating clockwise with angular speed 1.00 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?

2. L = Ltrans + Lrot
L = r x p
L = |r||p|sin(theta)
moment of inertia of a disk = (1/2)mr^2



3. Ok so i tried solving this by finding out the angular momentum of the disc which is <0,0,-1.458> but I cannot figure out the total before the impact. I don't think I solve this without the angle of impact but there has to be a solution. i think that afterwards the angular momentum of both will just be the same as the moment before the impact because momentum is conserved right?
 
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  • #2
i figured out that the direction is in the negative y cause the clay falls on the disc but i still can't figure out either before or after the impact momentum
 
  • #3
figured out the momentum after the impact <0,0,1.458> still clueless about before the impact
 

1. What is angular momentum in a multiparticle system?

Angular momentum in a multiparticle system is a measure of the rotational motion of a group of particles around a common axis. It is a vector quantity that takes into account both the mass and velocity of each individual particle in the system.

2. How is angular momentum calculated in a multiparticle system?

Angular momentum in a multiparticle system is calculated by taking the cross product of the position vector and the momentum vector for each particle in the system, and then summing up these individual contributions.

3. What is the conservation of angular momentum in a multiparticle system?

The conservation of angular momentum in a multiparticle system states that the total angular momentum of the system remains constant unless acted upon by an external torque. This means that the sum of the individual angular momenta of the particles in the system remains the same over time.

4. How does angular momentum affect the stability of a multiparticle system?

Angular momentum plays a crucial role in determining the stability of a multiparticle system. In general, a higher angular momentum results in a more stable system, as it requires a greater force to change the rotational motion of the particles.

5. What are some real-world applications of angular momentum in multiparticle systems?

Angular momentum in multiparticle systems has many practical applications, such as in the fields of astrophysics, where it helps explain the rotational motion of planets and galaxies. It is also important in the design and operation of satellites and spacecraft, as well as in the development of new materials and technologies in engineering and mechanics.

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