CONCEPTS ROTATION + ANGULAR MOMENTUM

A disk is free to rotate about a fixed axis. A tangential force applied a distance d from the axis causes an angular acceleration α. What angular acceleration is produced if the same force is applied a distance 2d from the axis?

2α

A wheel rotates through 5.0 rad in 2.8 s as it is brought to rest with constant angular acceleration. Determine the wheel's initial angular speed before braking began.

3.6 rad/sec

Starting from rest and rotating at constant angular acceleration, a disk takes 10 revolutions to reach an angular speed ω. How many additional revolutions at the same angular acceleration are required for it to reach an angular speed of 2ω?

30 rev

What is the angular speed of Earth, in radians per second, as it rotates about its axis?

7.3 E-5 rad/sec

A cyclist accelerates uniformly from rest. After 8.0 s, the wheels have rotated 3.0 rev. (a) What is the angular acceleration of the wheels? (b) What is the angular speed of the wheels at the end of the 8.0 s?

A. 0.59 rad/s^2 B. 4.7 rad/sec

Disk B was identical to disk A before a hole was drilled though the center of disk B. Which disk has the largest moment of inertia about its symmetry axis center?

Because its mass is now greater than that of disk B, disk A has the larger moment of inertia about its axis of symmetry.

Two points are on a disk that is turning about a fixed-axis through its center, perpendicular to the disk and through its center, at increasing angular velocity. One point on the rim and the other point is halfway between the rim and the center. Which point has the greater centripetal acceleration?

Because r is greater for the point on the rim, it has the greater centripetal acceleration.

Two points are on a disk that is turning about a fixed-axis through its center, perpendicular to the disk and through its center, at increasing angular velocity. One point on the rim and the other point is halfway between the rim and the center. Which point has the greater speed?

Because r is greater for the point on the rim, it has the greater speed.

Two points are on a disk that is turning about a fixed-axis through its center, perpendicular to the disk and through its center, at increasing angular velocity. One point on the rim and the other point is halfway between the rim and the center. Which point moves the greater distance in a given time?

Because r is greater for the point on the rim, it moves the greater distance.

You are looking down from above at a merry-go-round, and observe that is rotating counterclockwise and its rotation rate is slowing. If we designate counterclockwise as positive, what is the sign of the angular acceleration?

Because the merry-go-round is slowing, the sign of its angular acceleration is NEGATIVE.

Two points are on a disk that is turning about a fixed-axis through its center, perpendicular to the disk and through its center, at increasing angular velocity. One point on the rim and the other point is halfway between the rim and the center. Which point has the greater angular acceleration?

Both have zero angular acceleration.

Two points are on a disk that is turning about a fixed-axis through its center, perpendicular to the disk and through its center, at increasing angular velocity. One point on the rim and the other point is halfway between the rim and the center. Which point has the greater angular speed?

Both points have the same angular speed.

Two points are on a disk that is turning about a fixed-axis through its center, perpendicular to the disk and through its center, at increasing angular velocity. One point on the rim and the other point is halfway between the rim and the center. Which point has the greater tangential acceleration?

Both points have zero tangential acceleration.

Two points are on a disk that is turning about a fixed-axis through its center, perpendicular to the disk and through its center, at increasing angular velocity. One point on the rim and the other point is halfway between the rim and the center. Which point turns through the greater angle?

Both points turn through the same angle.

Angular speed and linear velocity have the same dimensions.

False.

All parts of a wheel rotating about a fixed axis must have the same centripetal acceleration.

False. The centripetal acceleration at a point on a rotating wheel is directly proportional to its distance from the center of the wheel.

Chad and Tara go for a ride on a merry-go-round. Chad sits on a pony that is 2.0 m from the rotation axis, and Tara sits on a pony 4.0 m from the axis. The merry-go-round is traveling counterclockwise and is speeding up. Does Chad or Tara have the larger centripetal acceleration?

The centripetal acceleration of all points on the merry-go-round is given by ac= rω^2. Because she is farther from the rotation axis, Tara has the larger centripetal acceleration.

Chad and Tara go for a ride on a merry-go-round. Chad sits on a pony that is 2.0 m from the rotation axis, and Tara sits on a pony 4.0 m from the axis. The merry-go-round is traveling counterclockwise and is speeding up. Does Chad or Tara have the larger linear speed?

The linear speed of all points on the merry-go-round is given by v = rω. Because she is farther from the rotation axis, Tara has the larger linear speed.

Most doors knobs are designed so the knob is located on the side opposite the hinges (rather than in the cen ter of the door, for example). Explain why this practice makes doors easier to open?

The moment arm of the force (pull) on the knob increases with the radial distance of the knob from the rotation axis. The larger the moment arm the greater the torque for the same pull. Thus, with the knob farthest from the axis the pull is most effective in rotating the door.

Chad and Tara go for a ride on a merry-go-round. Chad sits on a pony that is 2.0 m from the rotation axis, and Tara sits on a pony 4.0 m from the axis. The merry-go-round is traveling counterclockwise and is speeding up. Does Chad or Tara have the larger tangential acceleration?

The tangential acceleration of all points on the merry-go-round is given by at = rα. Because the angular acceleration isthe same for all points on the merry-go-round and she is farther from the rotation axis, Tara has the larger tangential acceleration.

All parts of a wheel rotating about a fixed axis must have the same angular acceleration.

True. The angular acceleration of all points on the wheel is dω/dt.

All parts of a wheel rotating about a fixed axis must have the same angular speed.

True. The angular speed of all points on a wheel is dθ/dt.