Question

A potter's wheel (a solid, uniform disk) of mass 7.1 kg and radius 0.78 m spins about its central axis. A 0.51 kg lump of clay is dropped onto the wheel at a distance 0.65 m from the axis. Calculate the rotational inertia of the system (in kg*m^2).

Answer 1

Moment of inertia of uniform disc is given by: 1/2 MR2, where M is mass and R is radius.

Here, M=7.1 kg, r=0.78 m. So, moment of inertia of disc = 7.1*0.78*0.78/2 = 2.15982 kg m2

Aso, moment of inertia of point mass = md2, where m is the mass of point mass and d is its distance from the axis.

Here,clay acts as point mass with m = 0.51 kg and d=0.65 m.

So, moment of inertia of clay = 0.51*0.65*0.65 = 0.215475 kgm2.

So, total moment of inertia = 2.15982 + 0.215475 = 2.375295 kg m2.