Question

 

to change the rate of their rotation with virtually constant angular acceleration. Many introductory problems in rotational kinematics involve the motion of a particle with constant, nonzero angular acceleration. The kinematic equations for such motion can be written as

and

.

Here, the symbols are defined as follows:

• is the angular position of the particle at a time t.
•  is the initial angular position of the particle.
• is the angular velocity of the particle at a time t.
•  is the initial angular velocity of the particle.
•  is the angular acceleration of the particle.
•  is the time that has elapsed since the particle was located at its initial position.

In answering the following questions, assume that the angular acceleration is constant and nonzero: .

 

A)

True or false: The quantity represented by  is a function of time (i.e., is not constant).

	true
	false

B)

True or false: The quantity represented by  is a function of time (i.e., is not constant).

 

	true
	false

C)

True or false: The quantity represented by  is a function of time (i.e., is not constant).

 

	true
	false

D)

True or false: The quantity represented by  is a function of time (i.e., is not constant).

 

	true
	false

E)

Which of the following equations is not an explicit function of time ? Keep in mind that an equation that is an explicit function of time involves  as a variable.

 

F)

In the equation , what does the time variable  represent?

Choose the answer that is always true. Several of the statements may be true in a particular problem, but only one is always true.

 

	the moment in time at which the angular velocity equals
	the moment in time at which the angular velocity equals
	the time elapsed from when the angular velocity equals  until the angular velocity equals

G)

Consider two particles A and B. The angular position of particle A, with constant angular acceleration, depends on time according to . At time , particle B, which also undergoes constant angular acceleration, has twice the angular acceleration, half the angular velocity, and the same angular position that particle A had at time .

Which of the following equations describes the angular position of particle B?

H)

How long after the time  does the angular velocity of particle B equal that of particle A?

 

	The two particles never have the same angular velocity.