A flywheel of mass 120 kg with a radius of gyration of 0.45 m is accelerated uniformly from 1000 rpm to 2400 rpm. The driving torque is a constant 210 N·m and friction can be ignored. How long t does this take?
A pendulum is made of a uniform slender rod (2.5 kg, 1.3 m long) pivoted at its top end O, with a thin solid disc of mass 3.5 kg and radius 0.15 m fixed to its lower end. The disc swings in its own plane and its centre is 1.45 m below O. Find the mass moment of inertia IO of the pendulum about O.
A uniform slender rod of mass 5.5 kg and length 0.9 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the vertical force R that the pin exerts on the rod just after release.
A uniform slender rod of mass 5 kg and length 0.9 m is pinned at one end and released from rest in a horizontal position. 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 solid cylinder of mass 16.5 kg rolls without slipping at 3.5 m/s. What percentage p of its total kinetic energy is rotational?
A thin hoop starts from rest and rolls without slipping down a slope inclined at 25° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 9.5 m along the slope.
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