A flywheel of mass 170 kg with a radius of gyration of 0.35 m is accelerated uniformly from 300 rpm to 1800 rpm. This takes 18 s. Ignoring friction, find the constant torque T needed.
A uniform slender rod of mass 6.5 kg and length 2.6 m rotates about an axis O perpendicular to the rod, 0.45 m from its centre G. Find its mass moment of inertia IO about that axis.
A uniform slender rod of mass 2.5 kg and length 2.3 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the acceleration atip of the free end just after release.
A flywheel with a moment of inertia of 17 kg·m² spins at 2900 rpm. A brake applies a constant friction torque of 60 N·m. How long t does it take to stop?
A uniform slender rod of mass 4.5 kg and length 1.3 m hangs at rest from a frictionless pivot at its top end. A 20 g bullet moving horizontally at 460 m/s hits the rod 0.52 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 33 kg, radius 0.15 m) spins freely at 1050 rpm about a vertical frictionless shaft. A thin ring of mass 12 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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