A pendulum is made of a uniform slender rod (0.5 kg, 0.9 m long) pivoted at its top end O, with a solid sphere of mass 8.5 kg and radius 0.05 m fixed to its lower end. The centre of the sphere is 0.95 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel of mass 50 kg with a radius of gyration of 0.1 m is accelerated uniformly from rest to 1900 rpm. This takes 21 s. Ignoring friction, find the constant torque T needed.
A motor delivers a torque of 1130 N·m at 1500 rpm. Find its power output P in kW.
A uniform slender rod of mass 7.5 kg and length 2.4 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 slender rod of mass 3 kg and length 0.8 m hangs at rest from a frictionless pivot at its top end. A 10 g bullet moving horizontally at 360 m/s hits the rod 0.67 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.
A uniform slender rod of mass 6.5 kg and length 0.5 m hangs at rest from a frictionless pivot at its top end. A 10 g bullet moving horizontally at 560 m/s hits the rod 0.25 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.
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