A pendulum is made of a uniform slender rod (4.5 kg, 1.5 m long) pivoted at its top end O, with a solid sphere of mass 1.5 kg and radius 0.25 m fixed to its lower end. The centre of the sphere is 1.75 m below O. Find the mass moment of inertia IO of the pendulum about O.
A pendulum is made of a uniform slender rod (1.5 kg, 1.2 m long) pivoted at its top end O, with a thin solid disc of mass 3.5 kg and radius 0.05 m fixed to its lower end. The disc swings in its own plane and its centre is 1.25 m below O. Find the mass moment of inertia IO of the pendulum about O.
A shaft transmits 141.5 kW at 1700 rpm. Find the torque T in the shaft.
A uniform slender rod of mass 6.5 kg and length 1.4 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 2 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 slender rod of mass 6.5 kg and length 0.7 m hangs at rest from a frictionless pivot at its top end. A 40 g bullet moving horizontally at 380 m/s hits the rod 0.58 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.
A solid sphere starts from rest and rolls without slipping down a slope inclined at 30° 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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