A pendulum is made of a uniform slender rod (1.5 kg, 0.8 m long) pivoted at its top end O, with a solid sphere of mass 1.5 kg and radius 0.05 m fixed to its lower end. The centre of the sphere is 0.85 m below O. Find the mass moment of inertia IO of the pendulum about O.
A uniform slender rod of mass 8.5 kg and length 0.5 m rotates about an axis O perpendicular to the rod, 0.05 m from its centre G. Find its mass moment of inertia IO about that axis.
A flywheel with a moment of inertia of 20.5 kg·m² spins at 2300 rpm. A brake applies a constant friction torque of 160 N·m. How many revolutions N does the flywheel make before it stops?
A uniform slender rod of mass 18.5 kg and length 2.3 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the acceleration atip of the free end just after release.
A solid sphere starts from rest and rolls without slipping down a slope inclined at 15° to the horizontal. Use g = 9.81 m/s². Its radius is 0.05 m. Find its angular velocity ω after it has rolled 9 m along the slope.
A hollow sphere starts from rest and rolls without slipping down a slope inclined at 10° to the horizontal. Use g = 9.81 m/s². Its radius is 0.35 m. Find its angular velocity ω after it has rolled 5 m along the slope.
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