A pendulum is made of a uniform slender rod (4 kg, 0.5 m long) pivoted at its top end O, with a thin solid disc of mass 6 kg and radius 0.1 m fixed to its lower end. The disc swings in its own plane and its centre is 0.6 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, 1 m long) pivoted at its top end O, with a solid sphere of mass 8 kg and radius 0.15 m fixed to its lower end. The centre of the sphere is 1.15 m below O. Find the mass moment of inertia IO of the pendulum about O.
A flywheel with a moment of inertia of 34 kg·m² spins at 800 rpm. A brake applies a constant friction torque of 60 N·m. How long t does it take to stop?
A flywheel with a moment of inertia of 6 kg·m² spins at 2500 rpm. A brake applies a constant friction torque of 125 N·m. How many revolutions N does the flywheel make before it stops?
A uniform slender rod of mass 10 kg and length 0.8 m hangs at rest from a frictionless pivot at its top end. A 15 g bullet moving horizontally at 580 m/s hits the rod 0.72 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.
A solid cylinder starts from rest and rolls without slipping down a slope inclined at 20° to the horizontal. Use g = 9.81 m/s². Its radius is 0.35 m. Find its angular velocity ω after it has rolled 7 m along the slope.
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