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Flywheel

A typical experiment in our laboratories is to determine the moment of inertia of a flywheel about its axis of rotation.

A flywheel is a heavy wheel with a long axle which is mounted horizontally on two ball bearings. The wheel is set into rotation about the horizontal axis by descent of a mass m suspended by a string wrapped around the axle. Suppose the mass descends a distance h when it (or string) leaves the axle; the potential energy loss is mgh. This energy is converted partly into kinetic energies of translation ½ mv² of falling mass and of rotation ½ I ω² of flywheel, and partly dissipated against friction. (Note that v = ω R, where R is radius of axle; at the instant mass leaves the flywheel, its linear velocity is equal to linear velocity of point of contact of other end fo the string leaving the surface of axle.) Assuming that flywheel performs steady work W per revolution against friction (at ball-bearing etc.), the conservation of energy implies,

mgh = ½ mv² + ½ I ω² + n₁ W

where, n₁ is number of rotations made by flywheel till the mass detaches.

After the mass has detached, suppose flywheel makes another n₂ rotations (in time t) before it stops due to friction. Hence we get

½ I ω² = n₂ W

Eliminating W, we find

The angular velocity of wheel changes uniformly (due to constant frictional force) from ω to 0 in time t. Hence, its average angular velocity during retardation is given by

Substituting for ω and putting v = ω R, we get

The above expression can be used to experimentally determine MI of flywheel under the assumption that frictional force remains constant during entire motion.