Angular momentum conservation and center of mass

In summary, two equal mass bodies, M, are connected by a massless pole of length L and placed on a horizontal table at rest. At t=0, a bullet of mass m collides with the pole, resulting in a completely elastic collision. The solution involves using the equations of momentum conservation, angular momentum conservation, and energy conservation.
  • #1
Eitan Levy
259
11

Homework Statement


Two bodies with an equal mass of M are attached by a pole with no mass with a length of L. The system is placed on a horizontal table and at first it is at rest. At t=0 a bullet with a mass of m hits the pole, as described in the picture. The collision is completely elastic.
jeRQRBs.png


Homework Equations


Momentum conservation.
Angular momentum conservation.
Energy conservation

The Attempt at a Solution


Typing math here is a nightmare for me so I will attach a picture explaining what I tried:
LYJc5L7.png


Thanks a lot.
 

Attachments

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  • #2
Never mind - I got it.
 

1. What is angular momentum conservation?

Angular momentum conservation is a principle in physics that states that the total angular momentum of a system remains constant as long as there are no external torques acting on the system. This means that the product of an object's moment of inertia and its angular velocity will remain constant unless acted upon by an external force.

2. How is angular momentum conserved in a closed system?

In a closed system, angular momentum is conserved because there are no external torques acting on the system. This means that the initial angular momentum of the system will be equal to the final angular momentum of the system, even if there are changes in the objects' positions or velocities within the system.

3. What is the center of mass of a system?

The center of mass of a system is the point at which the mass of an object is evenly distributed, and there is no net torque acting on the system. It is the point around which the system's mass is evenly distributed, and it is often used to describe the motion of a system as a whole.

4. How is the center of mass related to angular momentum?

The center of mass is related to angular momentum because it is the point at which the total angular momentum of a system can be measured. It is also the point around which the system's angular momentum is constant, as long as there are no external torques acting on the system.

5. What is the significance of angular momentum conservation and the center of mass in everyday life?

Angular momentum conservation and the center of mass are important principles in understanding the motion of objects in our everyday lives. These principles can help us understand the orbits of planets, the motion of spinning objects, and the balance of objects. They are also crucial in fields such as engineering and astronomy, where precise understanding of motion is necessary.

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