14. Torque & Rotational Dynamics

The composite disc below is free to rotate about a fixed axis, perpendicular to it and through its center. All forces are 100 N, and all angles are 37°. The dotted lines are either exactly parallel or exactly perpendicular to each other. The inner (darker) and outer (lighter) discs have radii 3 m and 5 m, respectively. Calculate the Net Torque produced on the composite disc, about an axis perpendicular to it and through its center. Use +/– to indicate direction.

A square with sides 4 m long is free to rotate around an axis perpendicular to its face and through its center. All forces shown are 100 N and act simultaneously on the square. The angle shown is 30°. Calculate the Net Torque that the forces produce on the square, about its axis of rotation.

A cord connected at one end to a block which can slide on an inclined plane has its other end wrapped around a cylinder resting in a depression at the top of the plane as shown in Fig. 10–81. Determine the speed of the block after it has traveled 1.80 m along the plane, starting from rest.

(b) the coefficient of friction between all surfaces is μ = 0.035 . [Hint: In part (b) first determine the normal force on the cylinder, and make any reasonable assumptions needed.]

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"(II) An Atwood machine (Fig. 11–16) consists of two masses, m_A = 7.0kg and m_B = 8.2kg , connected by a cord that passes over a pulley free to rotate about a fixed axis. The pulley is a solid cylinder of radius R₀ = 0.45m and mass 0.80 kg.                                                                                                                                                                   

 (a) Determine the acceleration a of each mass.                                                                                                                                                 

 (b) What percentage of error in a would be made if the moment of inertia of the pulley were ignored? Ignore friction in the pulley bearings. Use angular momentum.

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(III) Two blocks are connected by a light string passing over a pulley of radius 0.15 m and moment of inertia I. The blocks move (towards the right) with an acceleration of 1.00 m/s² along their frictionless inclines (see Fig. 10–62).

(c) Find the net torque acting on the pulley, and determine its moment of inertia, I.

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(III) An Atwood machine consists of two masses, mₐ = 65 kg and m₈ = 75 kg, connected by a massless inelastic cord that passes over a pulley free to rotate, Fig. 10–63. The pulley is a solid cylinder of radius R = 0.45 m and mass 6.0 kg.

(a) Determine the acceleration of each mass.

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