Exam 8: Rotational Motion

A solid uniform ball of mass 1.0 kg and radius 1.0 cm starts from rest and rolls down a 1.0-m high ramp. There is enough friction on the ramp to prevent the ball from slipping as it rolls down. (a) What is the forward speed of the ball when it reaches the bottom of the ramp? (b) What would be the forward speed of the ball if there were no friction on the ramp? (c) Since the ball starts from the same height in both cases, why is the speed different?

A string is wrapped tightly around a fixed frictionless pulley that has a moment of inertia of 0.0352 $\mathrm { kg } \cdot \mathrm { m } ^ { 2 }$ and a radius of 12.5 cm. The string is pulled away from the pulley with a constant force of 5.00 N, causing the pulley to rotate. What is the speed of the string after it has unwound 1.25 m if the string does not slip on the pulley?

Express the angular speed of an old 33 1/3 rpm LP in rad/s.

A cinder block of mass m=4.0 kg is hung from a nylon string that is wrapped around a frictionless pulley having the shape of a cylindrical shell, as shown in the figure. If the cinder block accelerates downward at $4.90 \mathrm {~m} / \mathrm { s } ^ { 2 }$ when it is released, what is the mass M of the pulley?

The figure shows scale drawings of four objects, each of the same mass and uniform thickness, with the mass distributed uniformly. Which one has the greatest moment of inertia when rotated about an axis perpendicular to the plane of the drawing at point P ?

A uniform ball is released from rest on a no-slip surface, as shown in the figure. After reaching its Iowest point, the ball begins to rise again, this time on a frictionless surface. When the ball reaches its maximum height on the frictionless surface, it is

Initially, a small 2.0-kg rock is whirling at the end of a very thin string in a circular path of radius 0.75 m on a horizontal frictionless surface, as shown in the figure. The initial tangential speed of The rock was 5.0 m/s. The string has been slowly winding around a vertical rod, and a few seconds Later the length of the string has shortened to 0.25 m. What is the instantaneous speed of the mass at The moment the string reaches a length of 0.25 m?

A pencil that is 15.7 cm Iong is released from a vertical position with the eraser end resting on a table. The eraser does not slip as it tips over. Treat the pencil like a uniform rod. What is the angular speed of the pencil just before it hits the table?

Consider a solid uniform sphere of radius R and mass M rolling without slipping. Which form of its kinetic energy is larger, translational or rotational?

A 5.0-m radius playground merry-go-round with a moment of inertia of $2000 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 }$ is rotating freely with an angular speed of 1.0 rad/s. Two people, each of mass 60 kg, are standing right Outside the edge of the merry-go-round and suddenly step onto the edge with negligible speed Relative to the ground. What is the angular speed of the merry-go-round right after the two people Have stepped on?

An artificial satellite in a low orbit circles the earth every 98 minutes. What is its angular speed in rad/s?

In a laboratory experiment, a student brings up the rotational speed of a flywheel to 30.0 rpm. She then allows it to slow down on its own, and counts 240 revolutions before the apparatus uniformly comes to a stop. The moment of inertia of the flywheel is $0.0850 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 }$ What is the magnitude of the retarding torque on the flywheel?

A solid uniform disk is rolling without slipping along a horizontal surface with a speed of 4.5 m/s when it starts up a ramp that makes an angle of $25 ^ { \circ }$ with the horizontal. What is the speed of the disk after it has rolled 3.0 m up as measured along the surface of the ramp?

An electrical motor spins at a constant 2695.0 rpm. If the rotor radius is 7.165 cm, what is the linear acceleration of the edge of the rotor?

A force of 16.88 N is applied tangentially to a wheel of radius 0.340 m and causes an angular acceleration of $1.20 \mathrm { rad } / \mathrm { s } ^ { 2 }$ What is the moment of inertia of the wheel?

A solid uniform sphere is rolling without slipping along a horizontal surface with a speed of 5.5 m/s when it starts up a ramp that makes an angle o $25 ^ { \circ }$ 5° with the horizontal. What is the speed of The sphere after it has rolled 3.0 m up as measured along the surface of the ramp?

A ballerina spins initially at 1.5 rev/s when her arms are extended. She then draws in her arms to her body and her moment of inertia becomes $0.88 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 }$ and her angular speec increases to 4.0 rev/s. What was her initial moment of inertia?

A child is riding a merry-go-round that has an instantaneous angular speed of 1.25 rad/s and an angular acceleration o $0.745 \mathrm { rad } / \mathrm { s } ^ { 2 }$ The child is standing 4.65 m from the center of the Merry-go-round. What is the magnitude of the linear acceleration of the child?

The drive chain in a bicycle is applying a torque of 0.850 N . m to the wheel of the bicycle. The wheel has a moment of inertia of $0.100 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 }$ What is the angular acceleration of the wheel?

A uniform, solid, cylindrical flywheel of radius 1.4 m and mass 15 kg rotates at 2.7 rad/s. What is the magnitude of the flywheel's angular momentum?