Calculation of the moment of inertia of a body
We give here a
method for finding the moment of inertia of a uniform thin rod about the centre by calculation.
Consider a rod of mass m and
cross-sectional area A, and let r be the mass of the rod per unit
volume. Let the rod be divided into slices perpendicular to XY.
(See Figure
1).
For one elementary slice the moment of inertia about 0 is Aρdx.x2
For the whole rod:
Similar proofs may be carried out for other
simply shaped bodies.
Student investigation
A braking system on a wheel destroys the rotational kinetic energy of the wheel, converting it into heat.
Make an estimate of the forces in a bicycle braking system by finding the angle through which the wheels of a bike rotate after the brakes are applied. (It is suggested that the bike is mounted upside down or clear of the ground for this investigation.)
