An electric motor turns a flywheel through a drive belt that joins a pulley on t

Question

An electric motor turns a flywheel through a drive belt that joins a pulley on the motor and a pulley that is rigidly attached to the flywheel as shown in the figure below. The flywheel is a uniform disk with a mass of 49.0 kg and a radius R = 0.625 m. It turns on a frictionless axle. Its pulley has much smaller mass and a radius of 0.230 m. The tension Tu in the upper (taut) segment of the belt is 164 N, and the flywheel has a clockwise angular acceleration of 1.67 rad/s2. Find the tension in the lower (slack) segment of the belt.

Explanation / Answer

moment of inertia = (1/2) m R^2 = (1/2) * 49* 0.625^2 = 9.5703

total torque = inertia * ang acc

164 * 0.230 - T * 0.230 = 9.5703 * 1.67

T = 130 Newtons is the tension in the lower belt

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