A pendulum is made of a uniform slender rod (2.5 kg, 0.5 m long) pivoted at its top end O, with a solid sphere of mass 2.5 kg and radius 0.25 m fixed to its lower end. The centre of the sphere is 0.75 m below O. Find the mass moment of inertia IO of the pendulum about O.
A pendulum is made of a uniform slender rod (1 kg, 0.7 m long) pivoted at its top end O, with a solid sphere of mass 1.5 kg and radius 0.15 m fixed to its lower end. The centre of the sphere is 0.85 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 1.7 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the vertical force R that the pin exerts on the rod just after release.
A flywheel with a moment of inertia of 5.5 kg·m² spins at 1200 rpm. A brake applies a constant friction torque of 200 N·m. How long t does it take to stop?
A uniform solid disc (mass 25 kg, radius 0.3 m) spins freely at 200 rpm about a vertical frictionless shaft. A thin ring of mass 4 kg and the same radius is dropped onto it from rest, centred on the shaft, and the two quickly spin together. Find their common speed n2 in rpm.
A solid sphere of mass 4.5 kg rolls without slipping at 5.5 m/s. What percentage p of its total kinetic energy is rotational?
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