Rotational energy and mass



Rotational energy and mass

Consider a rigid body rotating about a fixed axis of rotation. The kinetic energy is by definition,

K( ½ Σi mi vi2 .

But we have already noted that the speed of the ith particle may be written in terms of the angular velocity of the body,

vi = ri(ω.

Making this substitution in the above sum gives,

K = ½ ω2 Σi miri(2.

The latter sum is by definition the rotational mass or moment of inertia of the rigid body,

I ( Σi miri(2 (discrete system)

I = ( r(2 dm (continuous system)

Often I is found by the parallel-axis theorem.

The kinetic energy is given the name rotational kinetic energy,

Krot = ½ I ω2 .

EXAMPLES[in class]

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