Is Angular Momentum Constant in the Body Frame of a Rigid Body?

In summary, the angular momentum of a rigid body, such as a disc, remains constant in both the lab frame and the body frame. This is true for simple bodies with 3D rotation, such as a rotating disc or a heavy top. However, when calculating the angular momentum about different points on the body, the values will be different and not equal to each other. To calculate the angular momentum about a specific point on the body, one must find the product of the angular velocity and the moment of inertia about that point.
  • #1
Ahmes
78
1
It might be a stupid question but I do want to make sure of that:
Angular momentum of a rigid body (such as a disc) is a constant vector in the lab frame.
It is a vector in the body frame too, is it constant in the body frame?

I refer to simple bodies with 3D rotation such as a rotationg disc or a heavy top.

Thanks in advance.
 
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  • #2
I am truly a stupid person - in its own frame a body does not rotate - right?
 
  • #3
one can calculate the angular momentum about any point on the body and it will be different about any point . i mean if L1 is angular momentum about one point and L2 is angular momentum about any other point (both the points are on body) then L1 will not be equal to L2 . To calculate angular momentum about any point on the body just find the product of angular velocity of the body and the MOI about that point (think why!)
 

FAQ: Is Angular Momentum Constant in the Body Frame of a Rigid Body?

What is angular momentum in a rigid body?

Angular momentum in a rigid body is a measure of the rotational motion of a body about a fixed axis. It is the product of the body's moment of inertia and its angular velocity.

How is angular momentum conserved in a rigid body?

According to the law of conservation of angular momentum, the total angular momentum of a rigid body remains constant unless acted upon by an external torque. This means that the angular momentum of a rigid body cannot be created or destroyed, only transferred between different parts of the body.

How does the distribution of mass affect angular momentum in a rigid body?

The distribution of mass in a rigid body affects the moment of inertia, which in turn affects the angular momentum. A body with a higher moment of inertia will have a higher angular momentum for the same angular velocity, and vice versa.

Can angular momentum change direction in a rigid body?

Yes, angular momentum in a rigid body can change direction. This can occur when there is a change in the direction of the axis of rotation, or when an external torque is applied to the body.

How is angular momentum related to rotational kinetic energy?

Angular momentum and rotational kinetic energy are related through the equation L = Iω, where L is angular momentum, I is the moment of inertia, and ω is the angular velocity. This relationship shows that an increase in angular momentum will result in an increase in rotational kinetic energy.

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