A box weighing 10 N rests on a horizontal table. A lightweight cord attached to the box passes through a cylindrical pulley with a mass of 1 kg and a diameter of 18 cm. A 6 N weight is suspended from the other end of the cord as shown in the image. After the system is released, determine the acceleration of the box.

A jewelry box of mass 1 kg is attached to the end of a thin string. The string is wound around a solid, uniform disk of mass 6 kg and radius 10 cm. The disk rotates about a fixed axis that passes through its center. What is the speed of the box right before hitting the ground if the box is released from rest from a height of 1m above the ground?

A Buddhist monk is holding a hand-held prayer wheel. A small metal ball of 0.20 kg is attached to the head of the prayer wheel by a string of length 0.19 m. The monk starts to move the prayer wheel which makes the metal ball move in a horizontal circle, accelerating it to a rotational speed of 66 rpm in 5.5 s from rest. Determine the magnitude and origin of the torque on the small ball.

A 55 kg athlete preparing to dive stands at the end of a homogenous horizontal diving board of mass 38 kg. The diving board is 6.0 m long. The other end is anchored through a screw to the diving tower. Calculate the magnitude of the torque exerted by the athlete and the board about the screw.  

A horizontal thin rod is free to rotate about point O. Point O is considered the origin of the x-y plane. The point of application of the force is located at x = 1.5 m, y = 1 m. If the force has a magnitude of 80.0 N and is directed 30º north of east, determine the net torque about O.

A sphere placed in a Cartesian frame at the position (1.5 m, 2.5 m, 0) is subject to a force F= -3 î N. Find the torque produced by F about the point O (0, 0, 0).

How can a 59-kg cyclist exert more torque while ascending a slope if he puts all his weight on each pedal? Given the pedals move in a circular path with a radius of 18 cm.

The motor of a hand-held sander machine applies a steady torque τ to the disk, enhancing its angular velocity by 1.5 rad/s each second. The moment of inertia of the disk is 3.0 kg•m². Calculate the torque τ.

A very light bar of length 0.80 m has two cubes of mass 0.25 kg and 0.75 kg welded to its two ends. The bar attached at its center of mass to a fan motor revolves counterclockwise at a steady angular speed of 45 rpm. A torque τ applied to the bar causes it to stop rotating in 12 s. Calculate τ.

A building employs a dual counterweight system with two elevator cars. Elevator Car A has a mass of 1200 kg and starts at the tenth floor. Elevator Car B, with a mass of 1250 kg, begins at the second floor. They are connected by a steel cable that runs over a pulley that is free to rotate about a fixed axis at the top of the shaft. The pulley is a solid cylinder with a radius of 0.80 meters and a mass of 100 kg. Find the acceleration of each elevator car as they move in the shaft.