I need help with #4 please An electric motor which supplies a constant torque is

Question

I need help with #4 please

An electric motor which supplies a constant torque is attached to a solid metal sphere of mass 25.0 kg and radius 6.0 cm. When the motor is turned on the ball accelerates at a constant rale. making 3 full nations in 5.0 seconds. What is the torque supplied by the motor? (0.54 N m) stick of length L free to rotate around one end has a moment of inertia of I = - 1/3 mL^2. The is held in a horizontal position and then released. What is the tangential acceleration of the stick; the instant after it is released. [14.7 m/s^2]

Explanation / Answer

Torque = Moment of inertia * angular acceleration

Moment of inertia of Sphere = 2/5 * Mr^2
Moment of inertia of Sphere = 2/5 * 25 * (6.0 * 10^-2)^2
Moment of inertia of Sphere = 0.036 Kg m^2

Angular acceleration = w^2*r
Where w = (3 * 2 * 3.14) / 5 = 3.768 rad/s

Angular Acceleration = 3.768 / 5 = 0.7536 rad^2/s

Torque = Moment of inertia * angular acceleration
Torque = 0.036 * 0.7536
Torque = 0.027 N-m

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