A pendulum is made of a uniform slender rod (4 kg, 0.8 m long) pivoted at its top end O, with a solid sphere of mass 1.5 kg and radius 0.05 m fixed to its lower end. The centre of the sphere is 0.85 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel of mass 190 kg with a radius of gyration of 0.4 m is accelerated uniformly from 400 rpm to 1200 rpm. The driving torque is a constant 180 N·m and friction can be ignored. How long t does this take?
A uniform slender rod of mass 6 kg and length 1.9 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the acceleration atip of the free end just after release.
A uniform slender rod of mass 10 kg and length 1 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find its angular acceleration α just after release.
A solid cylinder rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². Find the acceleration a of its centre.
A solid cylinder 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 6 m along the slope.
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