A pendulum is made of a uniform slender rod (0.5 kg, 0.5 m long) pivoted at its top end O, with a thin solid disc of mass 6 kg and radius 0.15 m fixed to its lower end. The disc swings in its own plane and its centre is 0.65 m below O. Find the mass moment of inertia IO of the pendulum about O.
A pendulum is made of a uniform slender rod (0.5 kg, 1.4 m long) pivoted at its top end O, with a thin solid disc of mass 8.5 kg and radius 0.1 m fixed to its lower end. The disc swings in its own plane and its centre is 1.5 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 36.5 kg·m² from rest up to 500 rpm in 25 s. Ignoring losses, find the average power Pavg it delivers, in kW.
A uniform slender rod of mass 6.5 kg and length 2.2 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 5 kg is fixed to its free end. Ignore friction and use g = 9.81 m/s². Find the speed v of the free end as the rod swings through the vertical position.
A solid cylinder starts from rest and rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 3 m along the slope.
A solid sphere starts from rest and rolls without slipping down a slope inclined at 30° to the horizontal. Use g = 9.81 m/s². Its radius is 0.2 m. Find its angular velocity ω after it has rolled 4.5 m along the slope.
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