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In summary, Angular Momentum and Torque are defined about a point, while Moment of Inertia of a body is defined about an axis. There are equations that relate Angular Momentum and Torque with Moment of Inertia. In the case of a body free to rotate in any axis, the general equations of motion should be considered, without limitations on a specific axis. The cross product of the position vector of the particle and its linear momentum is used to calculate angular momentum, with a specific point chosen as the reference point. The Moment of Inertia Tensor is a second-order tensor and can be reduced to a scalar by restricting the rotation to a specific axis. However, in the case of no limitations, the relevant component of torque is the only one

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According to whom?Nikhil_RG said:Angular Momentum and Torque are defined about a point. But Moment of Inertia of a body is defined about an axis.

Wikipedia:

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.

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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.

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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.

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Well, first of all, do you understand tensors?Nikhil_RG said:Orodruin , is there a textbook or resource that I could refer to to understand about Moment of Inertia Tensor.

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).Nikhil_RG said: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.

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.Nikhil_RG said: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.

Moment of inertia is a measure of an object's resistance to changes in its rotational motion. It is often defined as the sum of the products of each particle's mass and the square of its distance from the axis of rotation. In simpler terms, it describes how difficult it is to change an object's rotation.

The moment of inertia for a point mass can be calculated using the formula I = mr², where m is the mass and r is the distance from the axis of rotation. For more complex shapes, the moment of inertia can be calculated using integration or by using tables of known values for common shapes such as cylinders, spheres, and discs.

Torque is the measure of the force that causes an object to rotate. It is directly proportional to the moment of inertia and the angular acceleration of the object. In other words, the larger the moment of inertia, the more torque is needed to rotate the object.

The moment of inertia plays a crucial role in an object's stability. Objects with a larger moment of inertia are more resistant to changes in their rotational motion, making them more stable. This is why objects with a low center of mass, such as a pyramid, are more stable than objects with a high center of mass, such as a pencil.

Yes, the moment of inertia can be changed by altering the mass distribution of an object. For example, a figure skater can increase or decrease their moment of inertia by extending or pulling in their arms, respectively. This change in moment of inertia affects their rotational speed and allows them to perform different spins and movements on the ice.

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