Exam 11: Rolling, Torque, and Angular Momentum

A solid wheel with mass M, radius R, and rotational inertia MR²/2, rolls without sliding on a horizontal surface.A horizontal force F is applied to the axle and the center of mass has an acceleration a.The magnitudes of the applied force F and the frictional force f of the surface, respectively, are:

A wheel of radius 0.5 m rolls without sliding on a horizontal surface as shown.Starting from rest, the wheel moves with constant angular acceleration 6 rad/s².The distance in traveled by the center of the wheel from t = 0 to t = 3 s is:

Two objects are moving in the x, y plane as shown.The magnitude of their total angular momentum (about the origin O)is:

Two disks are mounted on low-friction bearings on a common shaft.The first disc has rotational inertia I and is spinning with angular velocity .The second disc has rotational inertia 2I and is spinning in the same direction as the first disc with angular velocity 11ef0073_0782_3eec_bc85_654df9a38a4a_TB6585_11 as shown.The two disks are slowly forced toward each other along the shaft until they couple and have a final common angular velocity of:

A 2.0-kg block travels around a 0.50-m radius circle with an angular speed of 12 rad/s.The circle is parallel to the xy plane and is centered on the z axis, a distance of 0.75 m from the origin.The z component of the angular momentum around the origin is:

A single force acts on a particle situated on the positive x axis.The torque about the origin is in the negative z direction.The force might be:

A 2.0-kg block starts from rest on the positive x axis 3.0 m from the origin and thereafter has an acceleration given by in m/s².At the end of 2.0 s its angular momentum about the origin is:

Possible units of angular momentum are:

A playground merry-go-round has a radius of 3.0 m and a rotational inertia of 600 kg∙m².It is initially spinning at 0.80 rad/s when a 20-kg child crawls from the center to the rim.When the child reaches the rim the angular velocity of the merry-go-round is:

When a man on a frictionless rotating stool extends his arms horizontally, his rotational kinetic energy:

When a woman on a frictionless rotating turntable extends her arms out horizontally, her angular momentum:

Which of the following is NOT a vector?

A particle is located on the x axis at x = 2.0 m from the origin.A force of 25 N, directed 30° above the x axis in the x-y plane, acts on the particle.What is the torque about the origin on the particle?

A block with mass M, on the end of a string, moves in a circle on a horizontal frictionless table as shown.As the string is slowly pulled through a small hole in the table:

A cylinder of radius R = 6.0 cm is on a rough horizontal surface.The coefficient of kinetic friction between the cylinder and the surface is 0.30 and the rotational inertia for rotation about the axis is given by MR²/2, where M is its mass.Initially it is not rotating but its center of mass has a speed of 7.0 m/s.After 2.0 s the speed of its center of mass and its angular velocity about its center of mass, respectively, are:

A 2.0-kg block travels around a 0.50-m radius circle with an angular velocity of 12 rad/s.The magnitude of its angular momentum about the center of the circle is:

A single force acts on a particle P.Rank each of the orientations of the force shown below according to the magnitude of the time rate of change of the particle's angular momentum about the point O, least to greatest.

A rod rests on frictionless ice.Forces that are equal in magnitude and opposite in direction are simultaneously applied to its ends as shown.The quantity that has a magnitude of zero is its:

When we apply the energy conversation principle to a cylinder rolling down an incline without sliding, we exclude the work done by friction because:

A 2.0-kg block travels around a 0.50-m radius circle with an angular speed of 12 rad/s.The circle is parallel to the xy plane and is centered on the z axis, 0.75 m from the origin.The component in the xy plane of the angular momentum around the origin has magnitude: