A pendulum is made of a uniform slender rod (5 kg, 1.5 m long) pivoted at its top end O, with a solid sphere of mass 9.5 kg and radius 0.2 m fixed to its lower end. The centre of the sphere is 1.7 m below O. Find the mass moment of inertia IO of the pendulum about O.
A uniform slender rod of mass 8 kg and length 0.6 m rotates about an axis O perpendicular to the rod, 0.2 m from its centre G. Find its mass moment of inertia IO about that axis.
A motor delivers a torque of 1800 N·m at 300 rpm. Find its power output P in kW.
A uniform slender rod of mass 7 kg and length 0.6 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 4.5 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 rolls without slipping down a slope inclined at 35° to the horizontal. Use g = 9.81 m/s². Find the acceleration a of its centre.
A uniform slender rod of mass 4 kg and length 1.4 m hangs at rest from a frictionless pivot at its top end. A 35 g bullet moving horizontally at 580 m/s hits the rod 0.86 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.
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