Question

A wheel with radius 0.4m is mounted on an axle and is free to rotate. Beginning with the wheel at rest, a string wrapped around the edge of the wheel, is pulled with a force of 20 N . While the string is unwinding the wheel rotates through an angle of 10 rad . If the angular speed of the wheel after the string is pulled is 4 rad/s , what is the moment of inertia of the wheel?

Answer 1

r = radius = 0.4 m

F = force = 20 N

$\theta$ = angular displacement = 10

W_i = initial angular velocity = 0 rad/s

W_f = Final angular velocity = 4 rad/s

$\alpha$ = angular acceleration = ?

Using the equation

W_f² = W_i² + 2 $\alpha$ $\theta$

4² = 0² + 2(10) $\alpha$

$\alpha$ = 0.8

Torque is given as

Fr = I $\alpha$

20 x 0.4 = I (0.8)

I = 10 kgm²