A string is wrapped around a uniform cylinder of mass M and radius R. The cylinder is released from rest with the string vertical and it's top-end tied to a fixed bar. Show that the tension in the string is one-third of the weight of the cylinder.
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A uniform solid cylinder of mass M and radius 2R rests on a horizontal tabletop. A string is attached by a yoke to a frictionless axle through the center of the cylinder so that the cylinder can rotate about the axle. The string runs over a disk-shaped pulley with mass M and radius R that is mounted on a frictionless axle through its center. A block of mass M is suspended from the free end of the string. The string doesn't slip over the pulley surface, and the cylinder rolls without slipping on the tabletop. Find the magnitude of the acceleration of the block after the system is released from the rest.
Figure P8.87
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A 21.1 g metal cylinder is placed on a turntable, with its center88.5 cm from the turntable's center. The coefficient of staticfriction between the cylinder and the turntable's surface is µs =0.623. A thin, massless string of length 88.5 cm connects thecenter of the turntable to the cylinder, and initially, the stringhas zero tension in it.Starting from rest, the turntable very slowly attains higher andhigher angular velocities, but the turntable and the cylinder canbe considered to have uniform circular motion at any instant.Calculate the tension in the string when the angular velocity ofthe turntable is 60 rpm (rotations per minute).
