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Mechanics

Rotational Dynamics

Consider the situation shown in the diagram below.

The force, F will provide a moment (or torque) given by

T = Fr

Assuming that there are no frictional (or other) forces opposing the motion of the wheel, the torque will cause the angular velocity of the wheel to change.

Experiments show that the rate of change of angular velocity is directly proportional to the torque.

Expressing this result as an equation we have

T = a constant × a

The constant is called the moment of inertia of the wheel and axle and is given the symbol I, so the equation is written

T = Ia

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The inertia of a body is a measure of its reluctance to change the state of its linear motion. Similarly, the moment of inertia of a body is its reluctance to change the state of its angular motion.

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© David Hoult 2008