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 T_u in the upper (taut) segment of the belt is 156 N, and the flywheel has a clockwise angular acceleration of 1.67 rad/s^2. Find the tension in the lower (slack) segment of the belt. N

Explanation / Answer

flywheel moment of inertia = 1/2*mR^2 = 1/2*77.5*0.625^2 = 15.14 kg m^2

torque = I*alpha = 15.14*1.67 = 25.3 Nm

torque = (Tu-Tb)*r

Tu-Tb = 25.3/0.23 = 109.9

Tb = 156-109.9 = 46.1 N

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