A pendulum is made of a uniform slender rod (1.5 kg, 0.8 m long) pivoted at its top end O, with a solid sphere of mass 6 kg and radius 0.05 m fixed to its lower end. The centre of the sphere is 0.85 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel of mass 170 kg with a radius of gyration of 0.35 m is accelerated uniformly from rest to 1400 rpm. The driving torque is a constant 130 N·m and friction can be ignored. How long t does this take?
A shaft transmits 27 kW at 2600 rpm. Find the torque T in the shaft.
A uniform slender rod of mass 2.5 kg and length 2.3 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 solid cylinder starts from rest and rolls without slipping down a slope inclined at 15° to the horizontal. Use g = 9.81 m/s². Its radius is 0.4 m. Find its angular velocity ω after it has rolled 9.5 m along the slope.
A hollow sphere rolls without slipping down a slope inclined at 20° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 4 m down the slope?
Full step-by-step solutions: practise this topic on examproblems.com.