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 77.5 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 is 165 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

M.I of disk = mr^2/2 = 15.14 kgm^2 Angular acceleration = a = 1.67 rad/s^2 Let tension in lower segment = Tl, then we get (Tu - Tl)*r = MI*a ... i.e, (165-Tl)*.230 = 15.14*1.67 on solving we get Tl = 55.07 N

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