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Mechanics

Factors which determine the Moment of Inertia of a body

1. The mass of the body. Experiments show that I is directly proportional to the mass.
2.

The distribution of mass in the body.

To illustrate this consider two wheels having equal mass but different mass distribution.

A

B

Imagine causing both of these wheels to accelerate from rest to the same angular velocity DOUBLEU in the same time t. The angular acceleration, SYGMA, must be the same for both wheels. Also, the total angle turned through must be the same for the two wheels.

But, when moving with angular velocity DOUBLEU, the particles of wheel B are moving faster than the particles of wheel A, so wheel B possesses more kinetic energy than wheel A. This means that there was more work done accelerating wheel B than accelerating wheel A.

Therefore, a greater torque was needed to accelerate B than A and so we must conclude that the moment of inertia of wheel B is greater than the moment of inertia of wheel A.

The moment of inertia of a body is directly proportional to its mass and increases as the mass is moved further from the axis of rotation.

The fact that I depends on mass distribution means that the same body can have different moments of inertia depending on which axis of rotation we consider.

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