A flywheel of mass 100 kg with a radius of gyration of 0.2 m is accelerated uniformly from rest to 1800 rpm. The driving torque is a constant 31 N·m and friction can be ignored. How long t does this take?
A flywheel of mass 100 kg has a radius of gyration of 0.55 m about its axis. It spins at 800 rpm. Find its kinetic energy Ek in kJ.
A uniform slender rod of mass 19.5 kg and length 0.9 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the vertical force R that the pin exerts on the rod just after release.
A uniform slender rod of mass 4.5 kg and length 1.9 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 4.5 kg is fixed to its free end. 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 uniform slender rod of mass 7.5 kg and length 0.8 m hangs at rest from a frictionless pivot at its top end. A 25 g bullet moving horizontally at 320 m/s hits the rod 0.47 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.
A uniform solid disc (mass 30 kg, radius 0.1 m) spins freely at 900 rpm about a vertical frictionless shaft. A thin ring of mass 9 kg and the same radius is dropped onto it from rest, centred on the shaft, and the two quickly spin together. Find their common speed n2 in rpm.
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