Exam 8: Rotational Kinematics

Two points are located on a rigid wheel that is rotating with decreasing angular velocity about a fixed axis. Point A is located on the rim of the wheel and point B is halfway between the rim and the axis. Which one of the following statements concerning this situation is true?

A satellite follows a circular path with constant speed around a planet. Which one of the following quantities is constant and non-zero for this satellite?

A 2.0-kg solid disk rolls without slipping on a horizontal surface so that its center proceeds to the right with speed 5.0 m/s. The point A is the uppermost point on the disk and the point B is along the horizontal line that connects the center of the disk to the rim. -What is the direction of the disk's angular velocity?

A wheel of radius 0.5 m rotates with a constant angular speed about an axis perpendicular to its center. A point on the wheel that is 0.2 m from the center has a tangential speed of 2 m/s. -Determine the tangential speed of a point 0.3 m from the center of the wheel.

Two motorcycles are riding around a circular track at the same angular velocity. One motorcycle is at a radius of 15 m; and the second is at a radius of 18 m. What is the ratio of their linear speeds, v₂^/v₁?

A bicycle travels 141 m along a circular track of radius 30 m. What is the angular displacement in radians of the bicycle from its starting position?

A 1.0-m roulette wheel reaches a maximum angular speed of 18 rad/s before it begins decelerating. After reaching this maximum angular speed, it turns through 35 revolutions (220 rad) before it stops. How long did it take the wheel to stop after reaching its maximum angular speed?

A long thin rod of length 2L rotates with a constant angular acceleration of 8.0 rad/s2 about an axis that is perpendicular to the rod and passes through its center. -What is the ratio of the tangential acceleration of a point on the end of the rod to that of a point a distance L/2 from the end of the rod?

A long thin rod of length 2L rotates with a constant angular acceleration of 8.0 rad/s2 about an axis that is perpendicular to the rod and passes through its center. -What is the ratio of the angular speed (at any instant) of a point on the end of the rod to that of a point a distance L/2 from the end of the rod?

On an amusement park ride, passengers are seated in a horizontal circle of radius 7.5 m. The seats begin from rest and are uniformly accelerated for 21 seconds to a maximum rotational speed of 1.4 rad/s. -What is the tangential acceleration of the passengers during the first 21 s of the ride?

A 0.254-m diameter circular saw blade rotates at a constant angular speed of 117 rad/s. What is the tangential speed of the tip of a saw tooth at the edge of the blade?

A long thin rod of length 2L rotates with a constant angular acceleration of 8.0 rad/s2 about an axis that is perpendicular to the rod and passes through its center. -What is the ratio of the tangential speed (at any instant) of a point on the end of the rod to that of a point a distance L/2 from the end of the rod?

A rigid body rotates about a fixed axis with a constant angular acceleration. Which one of the following statements is true concerning the tangential acceleration of any point on the body?

During the spin-dry cycle of a washing machine, the motor slows from 90 rad/s to 30 rad/s while the turning the drum through an angle of 180 radians. What is the magnitude of the angular acceleration of the motor?

A 2.0-kg solid disk rolls without slipping on a horizontal surface so that its center proceeds to the right with speed 5.0 m/s. The point A is the uppermost point on the disk and the point B is along the horizontal line that connects the center of the disk to the rim. -What is the instantaneous speed of point A with respect to the ground?