A pendulum is made of a uniform slender rod (1.5 kg, 1.1 m long) pivoted at its top end O, with a thin solid disc of mass 9.5 kg and radius 0.1 m fixed to its lower end. The disc swings in its own plane and its centre is 1.2 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel of mass 170 kg with a radius of gyration of 0.6 m is accelerated uniformly from 800 rpm to 1700 rpm. This takes 22 s. Ignoring friction, find the constant torque T needed.
A uniform slender rod of mass 17.5 kg and length 1.8 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 2 kg and length 1 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 angular velocity ω of the rod as it swings through the vertical position.
A solid sphere rolls without slipping down a slope inclined at 15° to the horizontal. Use g = 9.81 m/s². Find the acceleration a of its centre.
A uniform slender rod of mass 4 kg and length 1.2 m hangs at rest from a frictionless pivot at its top end. A 35 g bullet moving horizontally at 200 m/s hits the rod 0.98 m below the pivot and stays embedded. Use g = 9.81 m/s². Find the largest angle φ from the vertical through which the rod swings.
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