A pendulum is made of a uniform slender rod (4.5 kg, 1.1 m long) pivoted at its top end O, with a thin solid disc of mass 10 kg and radius 0.25 m fixed to its lower end. The disc swings in its own plane and its centre is 1.35 m below O. Find the mass moment of inertia IO of the pendulum about O.
A pendulum is made of a uniform slender rod (5 kg, 0.6 m long) pivoted at its top end O, with a thin solid disc of mass 1 kg and radius 0.15 m fixed to its lower end. The disc swings in its own plane and its centre is 0.75 m below O. Find the mass moment of inertia IO of the pendulum about O.
A motor brings a flywheel with a moment of inertia of 36 kg·m² from rest up to 900 rpm in 40 s. Ignoring losses, find the average power Pavg it delivers, in kW.
A uniform slender rod of mass 14 kg and length 1.5 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 2 kg and length 1.5 m hangs at rest from a frictionless pivot at its top end. A 15 g bullet moving horizontally at 320 m/s hits the rod 1.3 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.
A hollow sphere starts from rest and rolls without slipping down a slope inclined at 15° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 10 m along the slope.
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