A pendulum is made of a uniform slender rod (3 kg, 0.7 m long) pivoted at its top end O, with a solid sphere of mass 1 kg and radius 0.1 m fixed to its lower end. The centre of the sphere is 0.8 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel of mass 140 kg with a radius of gyration of 0.5 m is accelerated uniformly from 700 rpm to 1100 rpm. The driving torque is a constant 51 N·m and friction can be ignored. How long t does this take?
A flywheel with a moment of inertia of 37 kg·m² spins at 2200 rpm. A brake applies a constant friction torque of 25 N·m. How long t does it take to stop?
A uniform slender rod of mass 9 kg and length 1.3 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 hollow sphere of mass 6 kg rolls without slipping at 1 m/s. Find its total kinetic energy Ek.
A solid sphere rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μs that prevents it from slipping.
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