Undergrad Moment of Inertia about an axis and Torque about a point

[Nikhil_RG]

Angular Momentum and Torque are defined about a point. But Moment of Inertia of a body is defined about an axis. There are equations which connect Angular momentum and Torque with Moment of Inertia. How will this be consistent? When I say that the torque of a force acting on a body about a point causes it to rotate about an axis, which axis should be considered that includes the point about which the torque is acting.

 

[malawi_glenn]

Angular Momentum and Torque are defined about a point. But Moment of Inertia of a body is defined about an axis.

According to whom?

Wikipedia:
Angular momentum is a vector quantity (more precisely, a pseudovector) that represents the product of a body's rotational inertia and rotational velocity (in radians/sec) about a particular axis.

Torque is defined as the product of the magnitude of the force and the perpendicular distance of the line of action of a force from the axis of rotation.

 

[Orodruin]

Moment of inertia is not defined relative to an axis. It is defined relative to a point. However, it is an order 2 tensor and not a scalar. In order to obtain a scalar, you can restrict the rotation of a body to only be possible around a particular axis. In this case, only the torque’s component in the axis direction will be relevant and angular momentum will be parallel to the axis.

 

[Nikhil_RG]

Thank you malawi_glenn for the response.

My question comes from the fact that the basic expression to calculate angular momentum involves finding the cross product of the position vector of the particle and it's linear momentum. So there has to be a point about which the position vector is defined and the angular momentum would be calculated about that particular point.

 

[Nikhil_RG]

Orodruin , is there a textbook or resource that I could refer to to understand about Moment of Inertia Tensor.

And in the case where the body is free to rotate in any axis and a force is acting at some point on it, which causes a Torque, which axis do we consider, since there are no limitations.

 

[Orodruin]

Orodruin , is there a textbook or resource that I could refer to to understand about Moment of Inertia Tensor.

Well, first of all, do you understand tensors?

And in the case where the body is free to rotate in any axis and a force is acting at some point on it, which causes a Torque, which axis do we consider, since there are no limitations.

You do not consider an axis. You consider the general equations of motion. There are some simplified cases such as an object rotating freely around a fixed point an object not subject to any net force (just torques).

So there has to be a point about which the position vector is defined and the angular momentum would be calculated about that particular point.

In the case where you fix the rotational axis, only the torque in the axis’ direction is relevant. This component will not depend on which reference point you pick as long as you pick a point on the axis.