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physics 2211
MP13: Chapter 13
Due at 5:30pm on Thursday, November 15, 2007
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Angular Motion with Constant Acceleration
Learning Goal:
To understand the meaning of the variables that appear in the equations for rotational kinematics
with constant angular acceleration.
Rotational motion with a constant nonzero acceleration is not uncommon in the world around us. For instance, many
machines have spinning parts. When the machine is turned on or off, the spinning parts tend to change the rate of their
rotation with virtually constant angular acceleration. Many introductory problems in rotational kinematics involve
motion of a particle with constant nonzero angular acceleration. The kinematic equations for such motion can be
written as
and
. Here, the meaning of the symbols is as follows:
is the angular position of the particle at time
.
is the initial angular position of the particle.
is the angular velocity of the particle at time
.
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:
.
Part A
True or false: The quantity represented by
is a function of time (i.e., is not constant).
ANSWER:
true
false
Part B
True or false: The quantity represented by
is a function of time (i.e., is not constant).
ANSWER:
true
false
Keep in mind that
represents an initial value, not a variable. It refers to the angular position of an object at
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some initial moment.
Part C
True or false: The quantity represented by
is a function of time (i.e., is not constant).
ANSWER:
true
false
Part D
True or false: The quantity represented by
is a function of time (i.e., is not constant).
ANSWER:
true
false
The angular velocity
always varies with time when the angular acceleration is nonzero.
Part E
Which of the following equations is not an explicit function of time
? Keep in mind that an equation that is an
explicit funciton of time involves
as a variable.
ANSWER:
An equation that is not an explicit function of time is useful when you do not know or do not need the time.
Part 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.
ANSWER:
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
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
accelaration, has twice the angular acceleration, half the angular velocity, and the same angular position that particle
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