A pendulum is made of a uniform slender rod (1 kg, 0.8 m long) pivoted at its top end O, with a thin solid disc of mass 9 kg and radius 0.1 m fixed to its lower end. The disc swings in its own plane and its centre is 0.9 m below O. Find the mass moment of inertia IO of the pendulum about O.
A pendulum is made of a uniform slender rod (0.5 kg, 0.7 m long) pivoted at its top end O, with a solid sphere of mass 7.5 kg and radius 0.2 m fixed to its lower end. The centre of the sphere is 0.9 m below O. Find the mass moment of inertia IO of the pendulum about O.
An 8 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 12.5 kg and radius 0.15 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 16 kg·m² spins at 2900 rpm. A brake applies a constant friction torque of 125 N·m. How long t does it take to stop?
A solid sphere 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.
A uniform slender rod of mass 4.5 kg and length 0.7 m hangs at rest from a frictionless pivot at its top end. A 45 g bullet moving horizontally at 600 m/s hits the rod 0.28 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.
Full step-by-step solutions: practise this topic on examproblems.com.