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 solid disk with a mass of 87.0 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 136 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. IN

Explanation / Answer

flywheel: I = 1/2 * 87kg * (0.625m)^2 = 16.99 kg·m^2

(The pulley, hase "much smaller mass," was ignored.)

Then torque T = I* = 16.99kg·m^2 * 1.67rad/s^2 = 28.376 N·m.

Then 28.376 N·m = (136N - Tb) * 0.230m

123.3780 = 136 - Tb

Tb = 12.6219 N

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