Conservation of Angular and Linear Momentum

In summary, the conversation discusses the conservation of quantities in a student-platform system where the student jumps off a rotating platform. The question asks which quantities are conserved, and the answer is only angular momentum due to the external force from the platform's fixed axle. The conversation also clarifies that the conservation of angular momentum is only meaningful in relation to a reference point, and in this case, it is the axle of the platform.
  • #1
Jzhang27143
38
1

Homework Statement



A student initially stands on a circular platform that is free to rotate without friction about its center. The student jumps off tangentially, setting the platform spinning. Quantities that are conserved for the student-platform system as the student jumps include which of the following?

I. Linear Momentum
II. Angular Momentum
III. Kinetic Energy

Homework Equations



F = dp/dt, T = dl/dt

The Attempt at a Solution



The answer is only angular momentum. However, I do not understand why angular momentum is conserved but not linear momentum. Since the system consists of the student and the platform, the force of the student on the platform and the reaction force are internal forces. They don't contribute to external force or torque. Am I missing something?
 
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  • #2
Jzhang27143 said:

Homework Statement



A student initially stands on a circular platform that is free to rotate without friction about its center. The student jumps off tangentially, setting the platform spinning. Quantities that are conserved for the student-platform system as the student jumps include which of the following?

I. Linear Momentum
II. Angular Momentum
III. Kinetic Energy

Homework Equations



F = dp/dt, T = dl/dt

The Attempt at a Solution



The answer is only angular momentum. However, I do not understand why angular momentum is conserved but not linear momentum. Since the system consists of the student and the platform, the force of the student on the platform and the reaction force are internal forces. They don't contribute to external force or torque. Am I missing something?
If the platform were completely free to move, both would be conserved. But the center of the platform apparently doesn't move.
 
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  • #3
Jzhang27143 said:
Am I missing something?
You are missing the external force from the platform's axle, which is presumably attached to the ground. If it wasn't fixed in place, then linear momentum would be conserved.
 
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  • #4
The question isn't quite right, and that may lead to your confusion.
Angular momentum is only meaningful in terms of some reference point. In the present case, the question assumes that reference point is the axle of the platform. If you were to take any other reference point it would not be conserved.
Given the answers by Doc Al and SammyS, do you see why the axle is special here?
 
  • #5


I would like to clarify that conservation of angular and linear momentum is a fundamental principle in physics that states that the total angular and linear momentum of a system remains constant in the absence of external forces or torques. This means that in an isolated system, the total angular momentum and linear momentum before and after an event will be the same.

In the given scenario, the student jumping off the platform causes a change in the system's angular momentum as the platform starts to spin. However, the total angular momentum remains the same because the student's and the platform's angular momentum cancel out. This is because the student's angular momentum is in the opposite direction to that of the platform's, and they have equal magnitudes.

On the other hand, the linear momentum of the system is not conserved because the student's jump introduces an external force on the system. This external force causes a change in the system's linear momentum, and it is not conserved.

In summary, the conservation of angular and linear momentum is a fundamental principle that helps us understand the behavior of systems and the effects of external forces and torques on them. In this scenario, we can see that only angular momentum is conserved because the system is isolated from external torques.
 

1. What is the difference between angular momentum and linear momentum?

Angular momentum is a property of a rotating object, while linear momentum is a property of a moving object in a straight line.

2. How is angular momentum conserved?

Angular momentum is conserved when there is no external torque acting on a system. This means that the total angular momentum of a system remains constant, even if the objects within the system are rotating or moving.

3. What is the equation for calculating angular momentum?

The equation for angular momentum is L = Iω, where L is angular momentum, I is moment of inertia, and ω is angular velocity.

4. How does conservation of angular momentum apply to real-world situations?

Conservation of angular momentum applies to all rotating systems, such as planets orbiting the sun, spinning tops, and even the Earth's rotation. It also plays a crucial role in understanding the motion of particles on a microscopic level, such as electrons in an atom.

5. Can angular momentum be transferred between objects?

Yes, angular momentum can be transferred between objects through collisions or interactions. However, the total angular momentum of a closed system will always remain constant.

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