A pendulum is made of a uniform slender rod (5 kg, 0.5 m long) pivoted at its top end O, with a thin solid disc of mass 3 kg and radius 0.1 m fixed to its lower end. The disc swings in its own plane and its centre is 0.6 m below O. Find the mass moment of inertia IO of the pendulum about O.
A pendulum is made of a uniform slender rod (4 kg, 1.3 m long) pivoted at its top end O, with a thin solid disc of mass 2 kg and radius 0.15 m fixed to its lower end. The disc swings in its own plane and its centre is 1.45 m below O. Find the mass moment of inertia IO of the pendulum about O.
A uniform slender rod of mass 12.5 kg and length 2.7 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find its angular acceleration α just after release.
A uniform slender rod of mass 7 kg and length 0.5 m is pinned at one end and released from rest in a horizontal position. 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 solid disc (mass 8 kg, radius 0.25 m) spins freely at 600 rpm about a vertical frictionless shaft. A thin ring of mass 17 kg and the same radius is dropped onto it from rest, centred on the shaft, and the two quickly spin together. How much kinetic energy ΔE is lost in the process?
A hollow sphere starts from rest and rolls without slipping down a slope inclined at 25° to the horizontal. Use g = 9.81 m/s². Its radius is 0.2 m. Find its angular velocity ω after it has rolled 7 m along the slope.
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