A pendulum is made of a uniform slender rod (3 kg, 1.5 m long) pivoted at its top end O, with a solid sphere of mass 2.5 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 is a uniform solid disc of mass 70 kg and radius 0.2 m. It spins at 1800 rpm. Find its kinetic energy Ek in kJ.
A uniform slender rod of mass 9.5 kg and length 1.8 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the acceleration atip of the free end just after release.
A uniform slender rod of mass 6 kg and length 2 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 3.5 kg is fixed to its free end. 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 hollow sphere of mass 6 kg rolls without slipping at 3 m/s. Find its rotational kinetic energy Erot.
A uniform solid disc (mass 32 kg, radius 0.45 m) spins freely at 850 rpm about a vertical frictionless shaft. A thin ring of mass 8 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?
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