A pendulum is made of a uniform slender rod (2 kg, 0.5 m long) pivoted at its top end O, with a solid sphere of mass 5 kg and radius 0.1 m fixed to its lower end. The centre of the sphere is 0.6 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel of mass 10 kg with a radius of gyration of 0.45 m is accelerated uniformly from 300 rpm to 1200 rpm. The driving torque is a constant 7.1 N·m and friction can be ignored. How long t does this take?
A uniform slender rod of mass 10 kg and length 2.1 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 speed v of the free end as the rod swings through the vertical position.
A shaft transmits 39.5 kW at 1800 rpm. Find the torque T in the shaft.
A uniform slender rod of mass 8 kg and length 0.7 m hangs at rest from a frictionless pivot at its top end. A 15 g bullet moving horizontally at 460 m/s hits the rod 0.43 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.
A uniform slender rod of mass 6 kg and length 1.2 m hangs at rest from a frictionless pivot at its top end. A 10 g bullet moving horizontally at 520 m/s hits the rod 0.78 m below the pivot and stays embedded. Use g = 9.81 m/s². Find the largest angle φ from the vertical through which the rod swings.
Full step-by-step solutions: practise this topic on examproblems.com.