Exam 13: Rotation II: a Conservation Approach

A wheel (radius = 0.20 m) is mounted on a frictionless, horizontal axis. A light cord wrapped around the wheel supports a 0.50-kg object, as shown in the figure. When released from rest the object falls with a downward acceleration of 5.0 m/s². What is the rotational inertia of the wheel? ​ ​

A pendulum bob of mass m is set into motion in a circular path in a horizontal plane as shown in the figure. The square of the angular momentum of the bob about the vertical axis through the point P is

The rigid body shown is rotated about an axis perpendicular to the paper and through the point P. If M = 0.40 kg, a = 30 cm, and b = 50 cm, how much work is required to take the body from rest to an angular speed of 5.0 rad/s? Neglect the mass of the connecting rods and treat the masses as particles.

A solid sphere, a solid cylinder, and a hoop all have the same mass and radius. Each are sent down identical inclined planes starting from rest. Their kinetic energies at the bottom of the incline are Ksphere, Kcylinder, and Khoop. Which of the following is true?

Two blocks, m1 = 1.0 kg and m² = 2.0 kg, are connected by a light string as shown in the figure. If the radius of the pulley is 1.0 m and its rotational inertia is 5.0 kg⋅m², the acceleration of the system is ​ ​

A uniform cylinder of radius R, mass M, and length L rotates freely about a horizontal axis parallel and tangent to the cylinder, as shown below. The rotational inertia of the cylinder about this axis is ​ ​

A force F is applied to a cylindrical roll of paper of radius R and mass M by pulling on the paper as shown. The acceleration of the center of mass of the roll of paper (when it rolls without slipping) is ​ ​

The diagram below shows five cylinders, each cylinder rotating with constant angular velocity about its central axis. The magnitude of the tangential speed of one point of each cylinder is shown, along with each cylinder's radius and mass. Which cylinder has the largest angular momentum?

The rigid body shown rotates about an axis through its center of mass and perpendicular to the paper. If M = 2.0 kg and L = 80 cm, what is the kinetic energy of this object when its angular speed about this axis is equal to 5.0 rad/s? Neglect the mass of the connecting rod and treat the masses as particles.

When an object is effectively isolated from external torques, like an ice skater twirling on the tip of one skate, the angular momentum of the object

A thin rod of mass M and length L is struck at one end by a ball of clay of mass m, moving with speed v as shown in the figure. The ball sticks to the rod. After the collision, the angular momentum of the clay-rod system about A, the midpoint of the rod, is

A uniform sphere of radius R and mass M rotates freely about a horizontal axis that is tangent to an equatorial plane of the sphere, as shown below. The rotational inertia of the sphere about this axis is ​ ​

Four identical particles (mass of each = 0.24 kg) are placed at the vertices of a rectangle (2.0 m × 3.0 m) and held in those positions by four light rods which form the sides of the rectangle. What is the rotational inertia of this rigid body about an axis that passes through the center of mass of the body and is parallel to the shorter sides of the rectangle?

A particle whose mass is 2.0 kg moves in the xy plane with a constant speed of 3.0 m/s along the direction . What is its angular momentum (in kg⋅m²/s) relative to the point (0, 5.0) meters?

Two blocks of masses m1 and m² are connected by a light cord that passes over a pulley of mass M, as shown. Block m² slides on a frictionless horizontal surface. The blocks and pulley are initially at rest. When m1 is released, the blocks accelerate and the pulley rotates. ​ ​ Use this exhibit to answer the following question(s). -The total angular momentum of the system of the two blocks and the pulley relative to the axis of rotation of the pulley is

Two blocks of masses m1 and m² are connected by a light cord that passes over a pulley of mass M, as shown. Block m² slides on a frictionless horizontal surface. The blocks and pulley are initially at rest. When m1 is released, the blocks accelerate and the pulley rotates. ​ ​ Use this exhibit to answer the following question(s). -The total angular momentum of the system of the two blocks and the pulley relative to the axis of rotation of the pulley is

Four identical particles (mass of each = 0.40 kg) are placed at the vertices of a rectangle (2.0 m × 3.0 m) and held in those positions by four light rods which form the sides of the rectangle. What is the rotational inertia of this rigid body about an axis that passes through the mid-points of the longer sides and is parallel to the shorter sides?

A 3.0-kg particle has a position vector given by , where is in meters and t is in seconds. What is the angular momentum of the particle, in kg⋅m²/s, about the origin at t = 2 s?

A mass (M1 = 5.0 kg) is connected by a light cord to a mass (m² = 4.0 kg) which slides on a smooth surface, as shown in the figure. The pulley (radius = 0.20 m) rotates about a frictionless axle. The acceleration of m² is 3.5 m/s². What is the rotational inertia of the pulley? ​ ​

A puck on a frictionless air hockey table has a mass of 5.0 kg and is attached to a cord passing through a hole in the surface as in the figure. The puck is revolving at a distance 2.0 m from the hole with an angular velocity of 3.0 rad/s. The angular momentum of the puck (in kg⋅m²/s) is