A momentum wheel for dynamicsclass demonstrations is shown I

A momentum wheel for dynamics-class demonstrations is shown. It is basically a bicycle wheel modified with rim band-weighting, handles, and a pulley for cord startup. The heavy rim band causes the radius of gyration of the 3.2-kg wheel to be 275 mm. If a steady 45-N pull T is applied to the cord, determine the angular acceleration of the wheel. Neglect bearing friction.

Solution

Here,

mass ,m = 275 Kg

k = 275 mm = 0.275 m

T = 45 N

theta = 30 degree

r = 100 mm = 0.1 m

Using second law of motion

angular acceleration * moment of inertia = torque

m * k^2 * a = T * r * cos(theta)

275 *0.275^2 * a = 45 * 0.100 * cos(30)

solving for a

a = 0.187 rad/s^2

the angular acceleration of the wheel is 0.187 rad/s^2