A flywheel of mass 110 kg with a radius of gyration of 0.25 m is accelerated uniformly from 200 rpm to 1900 rpm. This takes 20 s. Ignoring friction, find the constant torque T needed.
A pendulum is made of a uniform slender rod (4 kg, 0.7 m long) pivoted at its top end O, with a thin solid disc of mass 8 kg and radius 0.05 m fixed to its lower end. The disc swings in its own plane and its centre is 0.75 m below O. Find the mass moment of inertia IO of the pendulum about O.
A motor delivers a torque of 250 N·m at 2500 rpm. Find its power output P in kW.
A uniform slender rod of mass 9.5 kg and length 1.3 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 1.5 kg is fixed to its free end. Ignore friction and use g = 9.81 m/s². Find the speed v of the free end as the rod swings through the vertical position.
A uniform solid disc (mass 12 kg, radius 0.45 m) spins freely at 700 rpm about a vertical frictionless shaft. A thin ring of mass 7 kg and the same radius is dropped onto it from rest, centred on the shaft, and the two quickly spin together. How much kinetic energy ΔE is lost in the process?
A thin hoop starts from rest and rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 7.5 m along the slope.
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