Question

A device is made of a wheel with an inner drum and is mounted on a frictionless axle so it does not translate but can rotate about its centre. As indicated in the figure, this device is used to lift a 30.0 kg box. The outer radius R of the device is 0.500 m and the radius of the inner drum is 0.200 m. A constant horizontal force F of magnitude 140 N is applied horizontally, as shown, to a massless rope wrapped around the rim of the wheel. Consequently, the box, which is suspended from another massless rope wrapped around the rim of the drum, has an upward acceleration of magnitude 0.800 m/s2 What is the rotational inertia (moment of inertia) of the device about its axis of rotation? [Assume that ropes do not slip.] Rope

Answer 1

T - mg = ma - (i) force equation for mass FR - T r = I alpha (ii) torque equation for pulley solving of I eliminating FR - mg r = I alpha + ma r I = FR - mg r - ma r/alpha = FR - mg r - ma r/a/r = FR r - mg r^2 - ma r^2/a I = (140) (0.5)(0.2) - (30) (9.8) (0.2)^2 - (30) (0.8) (0.2)^2/0.8 = 15.91 Hg m^2