The moment of inertia of a rolling object is the rotary analogy of mass and governs the rotary acceleration. It can be determined in three ways; by rolling, oscillation or direct calculation. All should ideally give the same result but the student can be introduced to differences caused by different experimental techniques
A pair of rails form an inclined track for a disc rolling on a spindle through its centre. The inclination of the track can be readily altered by raising an end fitted with a height bar. Two discs are supplied; the larger has a diameter of 150mm and a thickness of 22.5mm, whilst the smaller is 100mm by 20mm. This enables two moments of inertia to be used and calculated. The moments of inertia of the discs are determined from the time taken for the disc to roll down the slope.
They may also be found from a subsidiary experiment using an oscillating pendulum in which the disc spindles are supported on knife edge bearings and a pendulum is attached to the shaft. The moments of inertia are estimated from the periodic time of the assembly.
A third method is direct measurement and calculation.
To determine and compare the moment of inertia of a disc by three methods:-