A pendulum is made of a uniform slender rod (3.5 kg, 1.5 m long) pivoted at its top end O, with a thin solid disc of mass 7 kg and radius 0.15 m fixed to its lower end. The disc swings in its own plane and its centre is 1.65 m below O. Find the mass moment of inertia IO of the pendulum about O.
A pendulum is made of a uniform slender rod (5 kg, 0.5 m long) pivoted at its top end O, with a thin solid disc of mass 6 kg and radius 0.25 m fixed to its lower end. The disc swings in its own plane and its centre is 0.75 m below O. Find the mass moment of inertia IO of the pendulum about O.
A uniform slender rod of mass 7 kg and length 0.6 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 3.5 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 flywheel with a moment of inertia of 19.5 kg·m² spins at 1500 rpm. A brake applies a constant friction torque of 165 N·m. How many revolutions N does the flywheel make before it stops?
A uniform slender rod of mass 10 kg and length 1.2 m hangs at rest from a frictionless pivot at its top end. A 10 g bullet moving horizontally at 440 m/s hits the rod 1.13 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.
A hollow sphere rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μs that prevents it from slipping.
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