A pendulum is made of a uniform slender rod (1.5 kg, 0.6 m long) pivoted at its top end O, with a thin solid disc of mass 1.5 kg and radius 0.15 m fixed to its lower end. The disc swings in its own plane and its centre is 0.75 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 1.1 m rotates about an axis O perpendicular to the rod, 0.15 m from its centre G. Find its mass moment of inertia IO about that axis.
A uniform slender rod of mass 6.5 kg and length 2.1 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 5 kg is fixed to its free end. 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 10 kg and length 1 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 3 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 15° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μs that prevents it from slipping.
A solid cylinder of mass 12 kg rolls without slipping at 8 m/s. Find its rotational kinetic energy Erot.
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