A flywheel of mass 140 kg with a radius of gyration of 0.15 m is accelerated uniformly from 600 rpm to 1400 rpm. This takes 20 s. Ignoring friction, find the constant torque T needed.
A pendulum is made of a uniform slender rod (4.5 kg, 1.4 m long) pivoted at its top end O, with a solid sphere of mass 6 kg and radius 0.2 m fixed to its lower end. The centre of the sphere is 1.6 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel with a moment of inertia of 19 kg·m² spins at 1500 rpm. A brake applies a constant friction torque of 60 N·m. How long t does it take to stop?
A 3 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 19.5 kg and radius 0.5 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the speed v of the block after it has fallen 3 m.
A uniform slender rod of mass 1 kg and length 0.5 m hangs at rest from a frictionless pivot at its top end. A 40 g bullet moving horizontally at 460 m/s hits the rod 0.35 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.
A uniform slender rod of mass 8 kg and length 1.7 m hangs at rest from a frictionless pivot at its top end. A 35 g bullet moving horizontally at 140 m/s hits the rod 1.13 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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