A pendulum is made of a uniform slender rod (3 kg, 1 m long) pivoted at its top end O, with a solid sphere of mass 4 kg and radius 0.25 m fixed to its lower end. The centre of the sphere is 1.25 m below O. Find the mass moment of inertia IO of the pendulum about O.
A pendulum is made of a uniform slender rod (5 kg, 0.8 m long) pivoted at its top end O, with a solid sphere of mass 10 kg and radius 0.1 m fixed to its lower end. The centre of the sphere is 0.9 m below O. Find the mass moment of inertia IO of the pendulum about O.
A uniform slender rod of mass 19 kg and length 1.5 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 shaft transmits 48 kW at 1800 rpm. Find the torque T in the shaft.
A uniform solid disc (mass 33 kg, radius 0.45 m) spins freely at 1200 rpm about a vertical frictionless shaft. A thin ring of mass 17 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 2 kg and length 1.3 m hangs at rest from a frictionless pivot at its top end. A 10 g bullet moving horizontally at 500 m/s hits the rod 0.57 m below the pivot and stays embedded. Use g = 9.81 m/s². Find the largest angle φ from the vertical through which the rod swings.
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