6.2.1 Angular Displacement, Velocity, and Acceleration

Question 1

Angular Displacement, Velocity, and Acceleration

Answer 1

• Only considering a system’s (or object’s) center of mass does not account for its rotational motion.
• The orientation of a freely rotating object is described by its angle of rotation, q, from a fixed point.
• Angular velocity is the rate of change of q: and . Angular acceleration is the rate of change of w:and.
• Two quantities associated with uniform circular motion are the period, T, and the frequency,

Question 2

In order to achieve artificial gravity, a space station must rotate 15 complete revolutions in 30 seconds. Which of the following is the angular velocity of this interstellar outpost in radians per second?

Answer 2

pi

Question 3

On the following position graph, which point has the greatest angular velocity?

Answer 3

Point B

Question 4

Suppose that an object on a certain machine has an angular position as a function of time given by theta = theta0 + 24wot =16t^2. Which of the following is the angular acceleration of the object?

Answer 4

a = 32

Question 5

An out-of-shape businessman does not want to admit to his wife how poorly he performed during his workout. When she asks how far he jogged around the circular indoor track with a radius of 10.0 m, he answers that he jogged 40 rad. How far did he run around the track?

Answer 5

400 m

Question 6

In 1809, longing for a university classroom and a good physics text, a certain cook was out on the prairie, and wanted to make sure that her triangle was just the right shape for calling the hands back for dinner. This required that two of the angles of the triangle were pi/6. Unfortunately, she didn’t have a protractor measured in radians. Which of the following are the angles in degrees?

Answer 6

180/6

Question 7

The graph below gives the angular position as a function of time for a new top secret testing apparatus. Where is the angular acceleration a minimum?

Answer 7

Point B

Question 8

The planet Earth is, on average, 93,000,000 miles away from the Sun, in a nearly circlular orbit. Which of the following is the distance, in miles, that the Earth travels during its yearly voyage?

Answer 8

2pi(9.3*10^7)

Question 9

A certain fan blade turns at 10,000 rpm. Which of the following is the proper angular velocity of this fan in radians per second?

Answer 9

10,000 * 2pi / 60

Question 10

A mobile consists of three objects, each of slightly different shape and mass, each at different radii. The objects are constrained to move together about their various circles to complete a revolution together. The objects are labeled A, B, and C, with A being the closest to the center and the heaviest object, and C being the outermost and lightest object. Which of the three has the angular velocity of the greatest magnitude?

Answer 10

They all have the same angular velocity.