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Exam 11: Rolling, Torque, and Angular Momentum

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Question 21

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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) 1.1 m/s, 0
B) 1.1 m/s, 19 rad/s
C) 1.1 m/s, 98 rad/s
D) 1.1 m/s, 200 rad/s
E) 5.9 m/s, 98 rad/s

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Question 22

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A 15-g paper clip is attached to the rim of a phonograph record with a radius of 30 cm, spinning at 3.5 rad/s. The magnitude of its angular momentum is:

A) 1.4 * 10^-3 kg . m²/s
B) 4.7 *10^-3 kg .m²/s
C) 1.6 * 10^--2 kg.m²/s
D) 3.2 * 10^-1 kg . m²/s
E) 1.1 kg . m²/s

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Question 23

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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:

A particle, held by a string whose other end is attached to a fixed point C, moves in a circle on a horizontal frictionless surface. If the string is cut, the angular momentum of the particle about the point C:

A 6.0-kg particle moves to the right at 4.0 m/s as shown. The magnitude of its angular momentum about the point O is:

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:

The angular momentum vector of Earth, due to its daily rotation, is directed:

A playground merry-go-round has a radius R and a rotational inertia I. When the merry-go-round is at rest, a child with mass m runs with speed v along a line tangent to the rim and jumps on. The angular velocity of the merry-go-round is then:

A wheel,with rotational inertia I, mounted on a vertical shaft with negligible ratational inertia, is rotating with angular speed $\omega$ _0. A nonrotation wheel with rotational inertia 2I is suddenly dropped onto the same shaft as shown.. The resultant combination of the two wheels and shaft will rotate at:

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:

A man, with his arms at his sides, is spinning on a light frictionless turntable. When he extends his arms:

A man, holding a weight in each hand, stands at the center of a horizontal frictionless rotating turntable. The effect of the weights is to double the rotational inertia of the system. As he is rotating, the man opens his hands and drops the two weights. They fall outside the turntable. Then:

A wheel rolls without slipping along a horizontal road as shown. The velocity of the center of the wheel is represented by $\rightarrow$ . Point P is painted on the rim of the wheel. The instantaneous velocity of point P is:

A solid wheel with mass M, radius R, and rotational inertia MR²/2, rolls without sliding on a horizontial 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:

The coefficient of static friction between a certain cylinder and a horizontal floor is 0.40. If the rotational inertia of the cylinder about its symmetry axis is given by I = (1/2) MR², then the maximum acceleration the cylinder can have without sliding is:

As a 2.0-kg block travels around a 0.50-m radius circle it has 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 magnitude of its angular momentum around the origin is:

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:

The unit kg.m²/s can be used for:

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

A 2.0-kg stone is tied to a 0.50-m long string and swung around a circle at a constant angular velocity of 12 rad/s. The net torque on the stone about the center of the circle is: