A pendulum is made of a uniform slender rod (5 kg, 1 m long) pivoted at its top end O, with a thin solid disc of mass 5 kg and radius 0.1 m fixed to its lower end. The disc swings in its own plane and its centre is 1.1 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel of mass 100 kg with a radius of gyration of 0.35 m is accelerated uniformly from rest to 1200 rpm. This takes 3 s. Ignoring friction, find the constant torque T needed.
A uniform slender rod of mass 5.5 kg and length 2.4 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 1 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 6.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 18.5 kg and radius 0.45 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the acceleration a of the block.
A thin hoop starts from rest and rolls without slipping down a slope inclined at 35° to the horizontal. Use g = 9.81 m/s². Its radius is 0.2 m. Find its angular velocity ω after it has rolled 2.5 m along the slope.
A solid sphere of mass 6.5 kg rolls without slipping at 5 m/s. What percentage p of its total kinetic energy is rotational?
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