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 53.5 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 is173 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.

_________________N

Explanation / Answer

here are a lot of words in this problem, and they make it sound more complicated than it is.

flywheel: I = ½ * 53.5kg * (0.625m)² = 10.45kg·m²
(The pulley, having "much smaller mass," was ignored.)

Then torque = I* = 10.45kg·m² * 1.67rad/s² = 17.45 N·m.

Then 17.45 N·m = (173N - Tb) * 0.230m
75.87 = 173- Tb
Tb =97.13N

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