A flywheel of mass 90 kg with a radius of gyration of 0.25 m is accelerated uniformly from rest to 1900 rpm. The driving torque is a constant 51 N·m and friction can be ignored. How long t does this take?
A pendulum is made of a uniform slender rod (3.5 kg, 0.8 m long) pivoted at its top end O, with a solid sphere of mass 8.5 kg and radius 0.1 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.
A flywheel with a moment of inertia of 29 kg·m² spins at 1000 rpm. A brake applies a constant friction torque of 110 N·m. How many revolutions N does the flywheel make before it stops?
A 1.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 10.5 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 solid cylinder rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 9.5 m down the slope?
A uniform slender rod of mass 6.5 kg and length 1.1 m hangs at rest from a frictionless pivot at its top end. A 50 g bullet moving horizontally at 100 m/s hits the rod 0.99 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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