A pendulum is made of a uniform slender rod (4 kg, 0.4 m long) pivoted at its top end O, with a solid sphere of mass 2 kg and radius 0.2 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 uniform slender rod of mass 10 kg and length 2.1 m rotates about an axis O perpendicular to the rod, 0.9 m from its centre G. Find its mass moment of inertia IO about that axis.
A shaft transmits 177 kW at 2000 rpm. Find the torque T in the shaft.
A uniform slender rod of mass 6.5 kg and length 0.5 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 4 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 uniform solid disc (mass 19 kg, radius 0.2 m) spins freely at 350 rpm about a vertical frictionless shaft. A thin ring of mass 10 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 uniform slender rod of mass 9 kg and length 1 m hangs at rest from a frictionless pivot at its top end. A 35 g bullet moving horizontally at 300 m/s hits the rod 0.5 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.
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