A pendulum is made of a uniform slender rod (2.5 kg, 0.4 m long) pivoted at its top end O, with a thin solid disc of mass 6.5 kg and radius 0.15 m fixed to its lower end. The disc swings in its own plane and its centre is 0.55 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel is a uniform solid disc of mass 40 kg and radius 0.4 m. It spins at 500 rpm. Find its kinetic energy Ek in kJ.
A motor delivers a torque of 1110 N·m at 3000 rpm. Find its power output P in kW.
A flywheel with a moment of inertia of 31 kg·m² spins at 300 rpm. A brake applies a constant friction torque of 195 N·m. How many revolutions N does the flywheel make before it stops?
A uniform slender rod of mass 4.5 kg and length 2 m hangs at rest from a frictionless pivot at its top end. A 20 g bullet moving horizontally at 160 m/s hits the rod 2 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 10 kg and length 1.6 m hangs at rest from a frictionless pivot at its top end. A 25 g bullet moving horizontally at 520 m/s hits the rod 1.04 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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