Exam 10: Energy and Momentum in Rotating Systems

A puck on a frictionless air hockey table has a mass of 5.0 g 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 cord is then pulled from below, shortening the radius to 1.0 m. The new angular velocity (in rad/s) is:

Refer to Exhibit 10-1 below.Exhibit 10-1 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. The total angular momentum of the system of the two blocks and the pulley relative to the axis of rotation of the pulley is:

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

Halley's comet moves about the sun in an elliptical orbit with its closest approach to the sun being 0.59 A.U. and its furthest distance being 35 A.U. [1 Astronomical Unit (A.U.) is the Earth-sun distance.] If the comet's speed at closest approach is 54 km/s, what is its speed when it is farthest from the sun?

A skater extends her arms horizontally, holding a 5-kg mass in each hand. She is rotating about a vertical axis with an angular velocity of one revolution per second. If she drops her hands to her sides, what will the final angular velocity (in rev/s) be if her moment of inertia remains approximately constant at 5 kg.m², and the distance of the masses from the axis changes from 1 m to 0.1 m?

A solid sphere, spherical shell, solid cylinder and a cylindrical shell all have the same mass m and radius R. If they are all released from rest at the same elevation and roll without slipping, which reaches the bottom of an inclined plane first?

Five objects of mass m move at velocity at a distance r from an axis of rotation perpendicular to the page through point A, as shown below. The one that has zero angular momentum about that axis is:

The rigid object shown is rotated about an axis perpendicular to the paper and through point P. The total kinetic energy of the object as it rotates is equal to 1.4 J. If M = 1.3 kg and L = 0.50 m, what is the angular velocity of the object? Neglect the mass of the connecting rods and treat the masses as particles.

A cylindrical shell rolls without slipping down an incline as shown in the figure. The linear acceleration of its centre of mass is:

A hockey puck travelling at speed v on essentially frictionless ice collides with one end of a straight stick lying flat on the ice and sticks to that end. In this collision:

What is the angular momentum of the moon about the Earth? The mass of the moon is 7.35 * 1022 kg, the centre-to-centre separation of the Earth and the moon is 3.84 * 105 km, and the orbital period of the moon is 27.3 days. Ignore the small offset of the centre of mass of the system from the centre of the Earth in your calculation.

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:

A solid sphere (radius R, mass M) rolls without slipping down an incline as shown in the figure. The linear acceleration of its centre of mass is:

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) metres?

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?

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?

Five identical cylinders are each acted on by forces of equal magnitude. Which force exerts the biggest torque about the central axes of the cylinders?

A space station out beyond the solar system is rotating with constant angular velocity. A spaceship heading into the station along a diameter of the station, uses its rockets to brake, and then docks inside the station at its centre. When the spaceship docks, the angular momentum of the system consisting of the station and ship:

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.

The rigid body shown rotates about an axis through its centre 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.