A pendulum is made of a uniform slender rod (2.5 kg, 1.5 m long) pivoted at its top end O, with a solid sphere of mass 3.5 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 pendulum is made of a uniform slender rod (5 kg, 1.4 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 1.45 m below O. Find the mass moment of inertia IO of the pendulum about O.
A uniform slender rod of mass 7.5 kg and length 1.4 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 speed v of the free end as the rod swings through the vertical position.
A motor delivers a torque of 680 N·m at 1200 rpm. Find its power output P in kW.
A uniform slender rod of mass 4 kg and length 1 m hangs at rest from a frictionless pivot at its top end. A 45 g bullet moving horizontally at 280 m/s hits the rod 1 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.
A uniform solid disc (mass 4 kg, radius 0.25 m) spins freely at 350 rpm about a vertical frictionless shaft. A thin ring of mass 11 kg and the same radius is dropped onto it from rest, centred on the shaft, and the two quickly spin together. Find their common speed n2 in rpm.
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