Question

I can test a new wheel design by rolling it down a test ramp. I release a wheel of mass m=1.6 kg and radius r=0.37 m from rest at an initial height of h=6.7 m at the top of a test ramp. It smoothly rolls to the bottom without sliding. I measure the linear speed of the wheel at the bottom of the test ramp to be v=4.7 m/s. What is the rotational inertia of my wheel?

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Mass of the wheel = m = 1.6 kg

Radius of the wheel = r = 0.37 m

Moment of inertia of the wheel = I

Height from which the wheel is released = h = 6.7 m

Linear speed of the wheel at the bottom of the ramp = v = 4.7 m/s

Angular speed of the wheel at the bottom of the ramp =

= 12.7 rad/s

By conservation of energy the initial potential energy of the wheel is equal to the total kinetic energy of the wheel at the bottom of the wheel.

I = 1.085 kg.m²

Rotational inertia of the wheel = 1.085 kg.m²