A pendulum is made of a uniform slender rod (3 kg, 1.4 m long) pivoted at its top end O, with a solid sphere of mass 4.5 kg and radius 0.1 m fixed to its lower end. The centre of the sphere is 1.5 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel of mass 20 kg has a radius of gyration of 0.5 m about its axis. It spins at 900 rpm. Find its kinetic energy Ek in kJ.
A uniform slender rod of mass 10 kg and length 1.9 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 uniform slender rod of mass 3.5 kg and length 1.2 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 person stands on a frictionless turntable and holds a 1 kg dumbbell in each hand, 0.9 m from the axis. The person and turntable alone have a moment of inertia of 1.5 kg·m² about the axis. They turn at 60 rpm, then pull the dumbbells in to 0.25 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.
A uniform slender rod of mass 7 kg and length 1.2 m hangs at rest from a frictionless pivot at its top end. A 15 g bullet moving horizontally at 580 m/s hits the rod 0.63 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.
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