A pendulum is made of a uniform slender rod (4.5 kg, 0.4 m long) pivoted at its top end O, with a solid sphere of mass 8 kg and radius 0.1 m fixed to its lower end. The centre of the sphere is 0.5 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, 1.3 m long) pivoted at its top end O, with a solid sphere of mass 9.5 kg and radius 0.1 m fixed to its lower end. The centre of the sphere is 1.4 m below O. Find the mass moment of inertia IO of the pendulum about O.
A motor delivers a torque of 730 N·m at 2900 rpm. Find its power output P in kW.
A uniform slender rod of mass 4 kg and length 0.5 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 1.5 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 solid disc (mass 28 kg, radius 0.4 m) spins freely at 100 rpm about a vertical frictionless shaft. A thin ring of mass 11 kg and the same radius is dropped onto it from rest, centred on the shaft, and the two quickly spin together. Find their common speed n2 in rpm.
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. Find its speed v after it has rolled 6 m along the slope.
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