A pendulum is made of a uniform slender rod (2.5 kg, 0.8 m long) pivoted at its top end O, with a thin solid disc of mass 6.5 kg and radius 0.25 m fixed to its lower end. The disc swings in its own plane and its centre is 1.05 m below O. Find the mass moment of inertia IO of the pendulum about O.
A uniform slender rod of mass 6 kg and length 2.1 m rotates about an axis O perpendicular to the rod, 0.75 m from its centre G. Find its mass moment of inertia IO about that axis.
A uniform slender rod of mass 9.5 kg and length 2.8 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the vertical force R that the pin exerts on the rod just after release.
A uniform slender rod of mass 14.5 kg and length 2.2 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the acceleration atip of the free end just after release.
A solid sphere starts from rest and rolls without slipping down a slope inclined at 15° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 5 m along the slope.
A hollow sphere starts from rest and rolls without slipping down a slope inclined at 30° to the horizontal. Use g = 9.81 m/s². Its radius is 0.2 m. Find its angular velocity ω after it has rolled 5.5 m along the slope.
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