A pendulum is made of a uniform slender rod (0.5 kg, 0.5 m long) pivoted at its top end O, with a solid sphere of mass 1 kg and radius 0.25 m fixed to its lower end. The centre of the sphere is 0.75 m below O. Find the mass moment of inertia IO of the pendulum about O.
A pendulum is made of a uniform slender rod (2.5 kg, 1 m long) pivoted at its top end O, with a solid sphere of mass 5 kg and radius 0.15 m fixed to its lower end. The centre of the sphere is 1.15 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 2.5 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 shaft transmits 28 kW at 1300 rpm. Find the torque T in the shaft.
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 3.5 kg·m² about the axis. They turn at 50 rpm, then pull the dumbbells in to 0.15 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.
A solid sphere of mass 14.5 kg rolls without slipping at 9.5 m/s. Find its total kinetic energy Ek.
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