A pendulum is made of a uniform slender rod (2 kg, 0.7 m long) pivoted at its top end O, with a thin solid disc of mass 1.5 kg and radius 0.2 m fixed to its lower end. The disc swings in its own plane and its centre is 0.9 m below O. Find the mass moment of inertia IO of the pendulum about O.
A uniform slender rod of mass 1 kg and length 0.9 m rotates about an axis O perpendicular to the rod, 0.25 m from its centre G. Find its mass moment of inertia IO about that axis.
A flywheel with a moment of inertia of 25 kg·m² spins at 500 rpm. A brake applies a constant friction torque of 65 N·m. How long t does it take to stop?
A uniform slender rod of mass 1.5 kg and length 0.5 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 person stands on a frictionless turntable and holds a 2.5 kg dumbbell in each hand, 0.6 m from the axis. The person and turntable alone have a moment of inertia of 2 kg·m² about the axis. They turn at 25 rpm, then pull the dumbbells in to 0.15 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.
A hollow sphere starts from rest and rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². Its radius is 0.25 m. Find its angular velocity ω after it has rolled 6 m along the slope.
Full step-by-step solutions: practise this topic on examproblems.com.