Tension --- Equilibrium and Elasticity

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Gravity

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angular acceleration

In a pulley system, the time of descent of a 100 gram mass is found to be 35 seconds. The vertical distance is given as 120 cms. The radius of the pulley( in the form of a disc) is 5 cms. Mass of the pulley is unknown. Determine (a) angular acceleration of the pulley (b) number of revolutions it makes during this time (c) Torque acting on the pulley. (d) Mass of the pulley.

Dynamics of rotational motion

Atwoods Machine Two blocks, A and B are attached to each end of a cord attached to a pulley C. Block A hangs slightly higher than Block B. Find the linear accelerations of block A and B, and the angular acceleration of the wheel C and the tension in each side of the cord if there is no slipping between the cord and the surface of the wheel. The masses of blocks A and B are Ma and Mb, respectively, the moment of inertia of the wheel about its axis is I, and the radius of the semicircle in which the string moves is R

Dynamics

A uniform, solid cylinder with 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 radis 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 doesnt slip over the pulley surface, and the cylinder rolls without slipping on the table top. Find the magnitude of the acceleration of the block after the system is released from rest.