A pendulum is made of a uniform slender rod (0.5 kg, 1.1 m long) pivoted at its top end O, with a thin solid disc of mass 4.5 kg and radius 0.2 m fixed to its lower end. The disc swings in its own plane and its centre is 1.3 m below O. Find the mass moment of inertia IO of the pendulum about O.
A pendulum is made of a uniform slender rod (2 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 10 kg and length 0.6 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 shaft transmits 18 kW at 1400 rpm. Find the torque T in the shaft.
A thin hoop of mass 3.5 kg rolls without slipping at 8 m/s. What percentage p of its total kinetic energy is rotational?
A thin hoop starts from rest and rolls without slipping down a slope inclined at 15° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 7.5 m along the slope.
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