Tire with a radius of?

Question

.30 m and mass of 1.1 kg is rotating at 93.6 rad/s. What torque is necessary to stop the tire in 1.72s ? Answer in uits of N.m

Answer 1

You need the moment of inertia of the tire about the rotation axis to determine how difficult it is to stop this tire. A tire with its mass concentrated near its radius is harder to stop than a solid tire of the same mass.

The moment of inertia for non-point objects can also be found or approximated as the product of three terms:
I = k m r^2

k = inertial constant
m = mass
r = radius of object from center of mass

For your problem, I'm going to assume the simplest case -- a thin-walled tire (where all of its mass is concentrated along the radius). So that makes k = 1.

This simplifies the inertia into:
I = m r^2 = 1.1 * 0.3^2 = 0.099 kg m^2

The angular momentum of your tire is:
L = I w (where w is the angular velocity)
L = 0.099 * 93.6 = 9.2664

Torque = (change in L) / (change in time)
T = 9.2664 / 1.72 = 5.389 N-m