A pendulum is made of a uniform slender rod (3 kg, 0.5 m long) pivoted at its top end O, with a thin solid disc of mass 1.5 kg and radius 0.05 m fixed to its lower end. The disc swings in its own plane and its centre is 0.55 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel of mass 70 kg has a radius of gyration of 0.35 m about its axis. It spins at 2000 rpm. Find its kinetic energy Ek in kJ.
A 13 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 12 kg and radius 0.4 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 flywheel with a moment of inertia of 38.5 kg·m² spins at 1900 rpm. A brake applies a constant friction torque of 90 N·m. How long t does it take to stop?
A solid cylinder 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 thin hoop rolls without slipping down a slope inclined at 10° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μs that prevents it from slipping.
Full step-by-step solutions: practise this topic on examproblems.com.