A pendulum is made of a uniform slender rod (4 kg, 0.9 m long) pivoted at its top end O, with a solid sphere of mass 7.5 kg and radius 0.15 m fixed to its lower end. The centre of the sphere is 1.05 m below O. Find the mass moment of inertia IO of the pendulum about O.
A pendulum is made of a uniform slender rod (3.5 kg, 0.7 m long) pivoted at its top end O, with a thin solid disc of mass 8 kg and radius 0.1 m fixed to its lower end. The disc swings in its own plane and its centre is 0.8 m below O. Find the mass moment of inertia IO of the pendulum about O.
A uniform slender rod of mass 3.5 kg and length 1.4 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 3 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 motor brings a flywheel with a moment of inertia of 38.5 kg·m² from rest up to 1900 rpm in 26 s. Ignoring losses, find the average power Pavg it delivers, in kW.
A uniform slender rod of mass 5.5 kg and length 1.1 m hangs at rest from a frictionless pivot at its top end. A 10 g bullet moving horizontally at 260 m/s hits the rod 0.84 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 hollow sphere of mass 8 kg rolls without slipping at 3.5 m/s. Find its rotational kinetic energy Erot.
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