A pendulum is made of a uniform slender rod (1.5 kg, 0.4 m long) pivoted at its top end O, with a thin solid disc of mass 6 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 uniform slender rod of mass 4 kg and length 2 m rotates about an axis O perpendicular to the rod, 0.45 m from its centre G. Find its mass moment of inertia IO about that axis.
A flywheel with a moment of inertia of 9.5 kg·m² spins at 1400 rpm. A brake applies a constant friction torque of 170 N·m. How many revolutions N does the flywheel make before it stops?
A uniform slender rod of mass 6.5 kg and length 2.6 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the vertical force R that the pin exerts on the rod just after release.
A uniform solid disc (mass 13 kg, radius 0.15 m) spins freely at 950 rpm about a vertical frictionless shaft. A thin ring of mass 18 kg and the same radius is dropped onto it from rest, centred on the shaft, and the two quickly spin together. How much kinetic energy ΔE is lost in the process?
A hollow sphere starts from rest and rolls without slipping down a slope inclined at 35° to the horizontal. Use g = 9.81 m/s². Its radius is 0.2 m. Find its angular velocity ω after it has rolled 3.5 m along the slope.
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