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 80.5 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 152 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

torque about pulley = torque about flywheel Tensile force x radius of pulley = moment of inertia of flywheel x angular acceleration (T1 -T2) x radius= 0.5 x mass of flywheel x square of radius of flywheel x angular acceleration (T1-135) 0.23 = 0.5 x 80 x 0.625^2 x 1.67 T1 =21.5N

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