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

flywheel (solid disc) mass m = 53.4 kg, radius R = 0.625 m

pulley radius = 0.230 m, smaller mass and tension in the upper segment = 173 N
angular acceleration alpha = 1.67 rad/s2

here
torque about pulley is equal to the torque about fly wheel

about pulley Tau = ( T_upper - T_lower)( radius of pulley) = (T_u - T_l)0.23

about flywheel Tau = I*alpha I is moment of inertia = 1/2 mR^2
       = 0.5*m*R^2*alpha
       = 0.5*53.4*0.625^2*1.67
       = 17.42 Nm

==>    (T_u - T_l)0.23 = 17.42

    T_u - T_l = 75.74

   => T_L = 173-75.74 = 97.26 N

   the tension in the lower (slack) segment of the belt is 97.26 N

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