Conservation of Angular Momentum in a Three Mass System

In summary, the problem involves two masses connected by a rigid rod, rotating about the center of mass with a given angular velocity. After one of the masses collides with a stationary third mass, the system's angular momentum is conserved. The new center of mass must be taken into account when calculating the moment of inertia for the system after the collision. The angular velocity remains the same, but the position of the center of mass changes and must be carefully considered when calculating the moment of inertia.
  • #1
neelakash
511
1

Homework Statement



Two masses M each are connected by a rigid rod of negligible mass having length a.The CM of the system is stationary in a gravity free space and the system rotates about the CM. with angular velocity w.One of the rotating masses strikes a third stationary ball of mass M which sticks to it.What is the angular momentum of the three mass system before and after collision?

Homework Equations



The Attempt at a Solution



For the collision conservation of linear momentum will be applicable.
Mv=2Mv' or,v'=v/2=wa/4. From this w' can be calculated.

Prior collision,L=Iw where I is the MI of the two mass system.

After collision, L'=I'w'

Please check if I am correct.
 
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  • #2
the system will rotate about new center of mass. Check for the position of new center of mass!
 
  • #3
So,we are to be careful to calculate I for the second time.
Second time, CM will be a/3 rd distance away from the mass 2M.Accordingly,I will change.

But angular velocity would be same as w'.Right?
 
  • #4
There will be no linear momentum...
angular momentum will be conserved...
CM will change the position...
And if one wants to find w',one has to find I' carefully.
 

1. What is the definition of angular momentum?

Angular momentum is a measure of the rotational energy of an object, and is calculated by multiplying the moment of inertia (a measure of how difficult it is to change an object's rotational motion) by the angular velocity (the rate of change of the object's angular position).

2. What is the angular momentum problem in physics?

The angular momentum problem is a fundamental issue in classical mechanics, where the total angular momentum of a system should be conserved according to the laws of physics, but certain observations and experiments show that this is not always the case. This has led to the development of theories such as quantum mechanics to better explain and predict the behavior of particles at a small scale.

3. How is angular momentum related to torque?

Torque, or the rotational force applied to an object, is directly proportional to the change in angular momentum of that object. This means that a larger torque will result in a greater change in angular momentum, and vice versa.

4. Can angular momentum be negative?

Yes, angular momentum can be either positive or negative. The direction of the angular momentum vector (clockwise or counterclockwise) determines its sign, with positive angular momentum indicating a counterclockwise rotation and negative angular momentum indicating a clockwise rotation.

5. How does angular momentum affect the stability of an object?

Angular momentum plays a crucial role in the stability of an object. If an object has a large angular momentum, it will resist changes in its rotational motion, making it more stable. On the other hand, a decrease in angular momentum can lead to instability and potential tumbling or falling of the object.

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