DSM Module 12: Rotational Kinematics

A bicycle wheel rotates counterclockwise at a constant rate. You can use one of the wheel's spokes to measure the wheel's angular displacement, Delta theta. How is this angular displacement related to the radius of the wheel, r, and the arc length, s, along the circumference of the wheel?

Delta theta equals s over r

How do you measure 1 radian?

One radian is the angle at which the arc s has the same length as the radius r.

The graph shows the angular velocity of a bicycle wheel as a function of time. Take positive values of omega to represent counterclockwise measurements. From the graph, what can you determine about the wheel's angular acceleration, vector alpha? (Graph of line going downwards in a straight line)

The angular acceleration is constant and clockwise.

The graph shows the angular velocity of a bicycle wheel as a function of time. Take positive values of omega to represent counterclockwise measurements. From the graph, what can you determine about the wheel's angular acceleration, vector alpha? (Graph of straight line going upwards)

The angular acceleration is constant and counterclockwise.

The graph shows the angular velocity of a bicycle wheel as a function of time. Take positive values of omega to represent counterclockwise measurements. From the graph, what can you determine about the wheel's angular acceleration, vector alpha? (Graph of line getting flatter as time increases)

The angular acceleration is decreasing and counterclockwise.

The graph shows the angular velocity of a bicycle wheel as a function of time. Take positive values of omega to represent counterclockwise measurements. From the graph, what can you determine about the wheel's angular acceleration, vector alpha?

The angular acceleration is increasing and counterclockwise.

The graph shows the angular velocity of a bicycle wheel as a function of time. Take positive values of omega to represent counterclockwise measurements. From the graph, what can you determine about the wheel's angular acceleration, vector alpha? (Graph of line increasing exponentially as time increases)

The angular acceleration is increasing and counterclockwise.

A Blu-ray disc rotates counterclockwise and speeds up at a constant rate. How does the angular acceleration of point P compare to the angular acceleration of point Q?

The angular acceleration of point P is equal to the angular acceleration of point Q.

The graph shows the angular position of a bicycle wheel spoke as a function of time. Take positive values of theta to represent counterclockwise angular measurements. From the graph, what can you determine about the wheel's angular velocity, vector omega? (Graph going straight down linearly)

The angular velocity is constant and clockwise.

The graph shows the angular position of a bicycle wheel spoke as a function of time. Take positive values of theta to represent counterclockwise angular measurements. From the graph, what can you determine about the wheel's angular velocity, vector omega? (Graph goes upwards in a straight line)

The angular velocity is constant and counterclockwise.

The graph shows the angular position of a bicycle wheel spoke as a function of time. Take positive values of theta to represent counterclockwise angular measurements. From the graph, what can you determine about the wheel's angular velocity, vector omega? (Graph of a completely flat line)

The angular velocity is zero.

A Blu-ray disc rotates counterclockwise at a constant rate, as shown in the figure. How does the angular velocity of point P compare to the angular velocity of point Q?

The angular velocity of point P is equal to the angular velocity of point Q.

On a bicycle, two sprocket wheels are connected by a chain that moves with a constant linear velocity as shown. The moving chain makes the sprocket wheels rotate. If the front sprocket has a diameter that is twice as large as the diameter of the rear sprocket, how do their angular velocities compare?

The angular velocity of the front sprocket is half of the rear sprocket's angular velocity.

A brother and sister are riding on a merry-go-round at the park. The brother rides on the outer edge of the merry-go-round and the sister rides closer to the center. While the merry-go-round rotates with a constant angular velocity, who has the greatest centripetal (radial) acceleration?

The brother has the greatest centripetal (radial) acceleration.

A brother and sister are riding on a merry-go-round at the park. The brother rides on the outer edge of the merry-go-round and the sister rides closer to the center. While the merry-go-round rotates with an increasing angular velocity, who has the greatest tangential acceleration?

The brother has the greatest tangential acceleration.

A Blu-ray disc rotates counterclockwise at a constant rate, as shown in the figure. How does the linear velocity of point P compare to the linear velocity of point Q?

The linear velocity of point P is less than the linear velocity of point Q.

A Blu-ray disc rotates counterclockwise and speeds up at a constant rate. How does the tangential acceleration of point P compare to the tangential acceleration of point Q?

The tangential acceleration of point P is less than the tangential acceleration of point Q.

When an object is rotating, how is the tangential acceleration of a point on its outer edge (at a distance r from the axis of rotation) related to its angular acceleration?

a sub t equals r times alpha

A bicycle wheel rotates counterclockwise at a constant rate. What are the appropriate units for a measurement of the wheel's angular velocity?

rad/s

A bicycle wheel rotates counterclockwise and increases in angular velocity at a constant rate. What are the appropriate units for a measurement of the wheel's angular acceleration?

rad/s2

A bicycle wheel rotates counterclockwise at a constant rate. You can use one of the wheel's spokes to measure the wheel's angular displacement. What are the appropriate units for this measurement?

radians (rad)

When an object is rotating, how is the linear velocity of a point on its outer edge (at a distance r from the axis of rotation) related to its angular velocity?

v equals r times omega

A wheel is rotating counterclockwise, which we will define as the positive direction, at an angular velocity of 2 rad/s. If the wheel then experiences a clockwise angular acceleration of 1 rad/s2, what is the wheel's angular velocity 3 seconds later?

1 rad/s clockwise

A wheel with a 3-m radius rotates with constant angular velocity omega = 2 rad/s. During 1 second, what is the wheel's angular displacement?

2 rad

A wheel is rotating counterclockwise, which we will define as the positive direction, at an angular velocity of 2 rad/s. If the wheel then experiences a counterclockwise angular acceleration of 1 rad/s2, what is the wheel's angular velocity 3 seconds later?

5 rad/s counterclockwise

A wheel with a 3-m radius rotates on a stationary axle with constant angular velocity omega= 2 rad/s. During 1 second, what is the distance traveled by a point on the outer edge of the wheel?

6 m