A pendulum is made of a uniform slender rod (2 kg, 1.1 m long) pivoted at its top end O, with a solid sphere of mass 6 kg and radius 0.2 m fixed to its lower end. The centre of the sphere is 1.3 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel is a uniform solid disc of mass 300 kg and radius 0.75 m. It spins at 3000 rpm. Find its kinetic energy Ek in kJ.
A uniform slender rod of mass 2 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 flywheel with a moment of inertia of 37 kg·m² spins at 1800 rpm. A brake applies a constant friction torque of 100 N·m. How many revolutions N does the flywheel make before it stops?
A person stands on a frictionless turntable and holds a 1.5 kg dumbbell in each hand, 0.8 m from the axis. The person and turntable alone have a moment of inertia of 1.5 kg·m² about the axis. They turn at 45 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 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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