Torque & Acceleration (Rotational Dynamics) Practice Problems

You pull with your hand on a string wound around a cylinder of diameter 30 cm and weight 39 N. The cylinder is free to rotate around a horizontal axle passing through its center of mass. The 30 N applied force is directed toward the positive x-axis and pulls the string tangentially from the cylinder as shown in the image. Determine i) the magnitude and ii) the direction of the force that the axle exerts on the cylinder.

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 toy is designed so that when charged it stores rotational energy on a spherical ball of diameter  60 mm and mass 890 g distributed uniformly. The ball is pivoted using a frictionless axle passing through its center. A dent on the toy's body scratches the ball at a point on its center creating 0.0820 N friction force at the point of contact. Determine the angular acceleration of the ball.

A steam engine has its flywheel pivoted about a vertical axle through its center. The flywheel has a moment of inertia of 2200 kg•m², a radius of 1.80 m, and spins with insignificant friction. An engineer studying the flywheel applies a tangential 35.0 N force to the flywheel's circumference for 8.0 s. Determine the work done by the engineer on the flywheel it was at rest when the force was applied.

A string is wound around a pulley. The free end of the string is attached to a metallic block. The pulley has a mass of 8.50 kg, a radius of 220 mm, and behaves like a uniform cylinder. You release the block from rest and notice that the block unwinds a 17.0 m length of the string in 6.50 s. What is the string's tension?

A solid disk with a moment of inertia of 5.4kg•m² measured relative to its axis of rotation is required to spin at an angular speed of 850 rev/min. Determine the torque that will bring the disk to this speed within 4.50 s when the disk is initially at rest.

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 chocolate box of mass m₁ = 1 kg and an ice bucket of mass m₂ = 3 kg are connected by a rope over a pulley of radius 20 cm. The chocolate box rests on a frictionless horizontal table. The hanging ice bucket is released vertically from rest and reaches a speed of 2 m/s after 1 s. Let T₁ be the tension in the part of the cord attached to m₁ and T₂ be the tension in the part of the cord attached to m₂. Find the tension in each part of the rope.