A pendulum is made of a uniform slender rod (0.5 kg, 1.5 m long) pivoted at its top end O, with a solid sphere of mass 9 kg and radius 0.1 m fixed to its lower end. The centre of the sphere is 1.6 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel of mass 40 kg with a radius of gyration of 0.6 m is accelerated uniformly from rest to 1100 rpm. This takes 17 s. Ignoring friction, find the constant torque T needed.
A uniform slender rod of mass 9 kg and length 2 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 motor delivers a torque of 1610 N·m at 2200 rpm. Find its power output P in kW.
A uniform solid disc (mass 39 kg, radius 0.5 m) spins freely at 100 rpm about a vertical frictionless shaft. A thin ring of mass 6 kg and the same radius is dropped onto it from rest, centred on the shaft, and the two quickly spin together. How much kinetic energy ΔE is lost in the process?
A solid sphere starts from rest and rolls without slipping down a slope inclined at 35° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 1 m along the slope.
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