A pendulum is made of a uniform slender rod (2.5 kg, 0.6 m long) pivoted at its top end O, with a thin solid disc of mass 1.5 kg and radius 0.2 m fixed to its lower end. The disc swings in its own plane and its centre is 0.8 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel is a uniform solid disc of mass 300 kg and radius 0.25 m. It spins at 2000 rpm. Find its kinetic energy Ek in kJ.
A motor delivers a torque of 1510 N·m at 3000 rpm. Find its power output P in kW.
A uniform slender rod of mass 9 kg and length 2.3 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 2.5 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 1.5 kg and length 0.5 m hangs at rest from a frictionless pivot at its top end. A 35 g bullet moving horizontally at 580 m/s hits the rod 0.35 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.
A uniform slender rod of mass 5.5 kg and length 1.5 m hangs at rest from a frictionless pivot at its top end. A 50 g bullet moving horizontally at 400 m/s hits the rod 1.5 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.
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