Question

A large grinding wheel in the shape of a solid cylinder of radius 0.330 m is free to rotate on a frictionless, vertical axle. A constant tangential force of 260 N applied to its edge causes the wheel to have an angular acceleration of 0.836 rad/s².

(a) What is the moment of inertia of the wheel?
kg · m²

Answer 1

Solution:-

Given –

Radius (r) = 0.330 m

Tangential force (F) = 260 N

Angular acceleration (a) = 0.836 rad/s^2

The moment of inertia of the wheel is-

T = I*a = T = r*F

Putting given values in above equation,

0.330*260 = I*0.836

I = 102.63 kg.m2

The moment of inertia of the wheel is 102.63 kg.m2

The moment of inertia, otherwise known as the mass moment of inertia, angular mass or rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about rotational axis.

Its SI unit is – kg.m2