A pendulum is made of a uniform slender rod (3.5 kg, 0.5 m long) pivoted at its top end O, with a solid sphere of mass 6.5 kg and radius 0.25 m fixed to its lower end. The centre of the sphere is 0.75 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel of mass 200 kg with a radius of gyration of 0.15 m is accelerated uniformly from 200 rpm to 1900 rpm. The driving torque is a constant 53 N·m and friction can be ignored. How long t does this take?
A uniform slender rod of mass 16.5 kg and length 1.4 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 3 kg and length 3 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 sphere 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 10 m along the slope.
A uniform slender rod of mass 2 kg and length 0.5 m hangs at rest from a frictionless pivot at its top end. A 30 g bullet moving horizontally at 160 m/s hits the rod 0.4 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.
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