Rod, Clay, and an Inelastic Collision

In summary, the conversation discusses how to determine the translational and rotational motion of a rod after being struck by a clay ball. It is suggested to use conservation of linear momentum to find the translational velocity of the center of mass of the rod and conservation of angular momentum to find the angular velocity about the center of mass after collision. It is also mentioned that the motion of a rigid object can be described as a combination of its translational motion and rotation about its center of mass. Finally, it is noted that the total angular momentum of an object about any axis is the sum of its angular momentum about its center of mass and the angular momentum of its mass concentrated at its center of mass.
  • #1
e(ho0n3
1,357
0
Problem: A thin rod of mass M and length L rests on a frictionless table and is struck at a point L/4 from its center of mass by a clay ball of mass m moving at a speed v (the velocity vector is perpendicular to the rod). The ball sticks to the rod. Determine the translational and rotational motion of the rod after the collision.

I can use conservation of angular momentum to determine the rotational velocity of the rod and the clay about the center of mass of the rod. Then, I'd figure I could use this angular speed to find the velocity of the clay and then use conservation of linear momentum to find the velocity of the center of mass of the rod. According to my calculations, the center of mass of the rod is moving in the same direction of the velocity vector v. Does this make sense?
 
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  • #2
That seems like an awful lot of work to simply calculate the velocity of the center of mass after collision. Just use conservation of linear momentum throughout to calculate translational velocity. Use conservation of angular momentum to find the angular velocity about its new center of mass after collision.
 
  • #3
Gza said:
That seems like an awful lot of work to simply calculate the velocity of the center of mass after collision. Just use conservation of linear momentum throughout to calculate translational velocity. Use conservation of angular momentum to find the angular velocity about its new center of mass after collision.
Hmm...I thought the rotation was about the center of mass of the rod not about the center of mass of the system after collision. How do you figure?
 
  • #4
e(ho0n3 said:
Hmm...I thought the rotation was about the center of mass of the rod not about the center of mass of the system after collision. How do you figure?
The motion of a rigid object (such as the composite object "rod + putty") can be described as a translational motion of its center of mass plus a rotation about its center of mass.

You know how to find the speed of the center of mass after the collision: linear momentum is conserved.

To find the rotational speed about the cm, do this. First find where the cm is just at the instant of collision. Then find the angular momentum about the cm prior to the collision. Since it's conserved, that's also the angular momentum about the cm after the collision. Find the rotational inertia of the "rod + putty" about the cm, then use it to find [itex]\omega[/itex].
 
  • #5
Doc Al said:
The motion of a rigid object (such as the composite object "rod + putty") can be described as a translational motion of its center of mass plus a rotation about its center of mass.
I think you meant "can be BEST describe...", since motion is relative to a reference frame and the point in the frame I'm describing the motion from. When you use the phrase about its center of mass, I imagine the object is rotating about an axis going through the center of mass, but how do I know, in this problem for example, where the rotation axis is (I know it's not fixed in some location in space, but that is all I know).
To find the rotational speed about the cm, do this. First find where the cm is just at the instant of collision. Then find the angular momentum about the cm prior to the collision. Since it's conserved, that's also the angular momentum about the cm after the collision. Find the rotational inertia of the "rod + putty" about the cm, then use it to find [itex]\omega[/itex].
Let me get this clear: I should do all of my calculations (pre- and post-collion) taking the center of mass of the rod + putty as my reference point.
 
  • #6
translation plus rotation

e(ho0n3 said:
I think you meant "can be BEST describe...", since motion is relative to a reference frame and the point in the frame I'm describing the motion from.
As long as you realize that the motion of a rigid object is a combination of the motion of its cm plus its rotation about its cm.
When you use the phrase about its center of mass, I imagine the object is rotating about an axis going through the center of mass, but how do I know, in this problem for example, where the rotation axis is (I know it's not fixed in some location in space, but that is all I know).
I'm not saying that the object is in pure rotation about its center of mass. It's also translating.
Let me get this clear: I should do all of my calculations (pre- and post-collion) taking the center of mass of the rod + putty as my reference point.
I would, but I'm lazy. (All what caculations? It's just angular momentum.) As long as you realize that the total angular momentum of the object about any axis is the sum of its angular momentum about its center of mass plus the angular momentum of its mass (assumed concentrated at its center of mass), then you can use any axis. So, if you find the initial angular momentum about the cm, then that will equal the final angular momentum about the cm, which would equal [itex]I_{cm}\omega[/itex].
 

1. What is a rod?

A rod is a long, thin, and solid object that has a cylindrical or rectangular shape. It can be made of various materials such as metal, wood, or plastic.

2. What is clay?

Clay is a type of soil that is composed of small particles of decomposed rock. It is soft and malleable when wet, but becomes hard and brittle when dried or fired.

3. What is an inelastic collision?

An inelastic collision is a type of collision where the objects involved stick together and do not bounce off each other after impact. This results in a loss of kinetic energy and deformation of the objects.

4. How do rod and clay interact in an inelastic collision?

In an inelastic collision between a rod and clay, the rod will typically penetrate the clay and come to a stop. The clay will deform and wrap around the rod, resulting in a loss of kinetic energy for both objects.

5. What is the significance of studying rod, clay, and inelastic collisions?

Studying rod, clay, and inelastic collisions can help us understand the principles of energy conservation and momentum in physics. It also has practical applications in industries such as car manufacturing and sports equipment design.

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