The following table gives the angular speed of a rotating fan blade at various times as...
The following table gives the angular speed of a rotating fan blade at various times as it slows to a stop.
| Time (s) | Angular speed (rad/s) |
| 0 | 5.0 |
| 2.0 | 4.1 |
| 4.0 | 3.0 |
Part A
Find the average angular acceleration for the times t=0 to t=2.0s
Part B
Find the average angular acceleration for the times t=0 to t=4.0s.
Part C
Find the average angular acceleration for the times t=2.0s to t=4.0s.
Homework Answers
The concepts used to solve this problem are angular velocity and angular acceleration.
Use the relationship between initial and final angular velocity to get the change in angular velocity.
Use the relationship between initial and final time to get the change in time.
Use the relationship between change in angular velocity and change in time to get the angular accelerations for several cases.
The expression change in angular velocity is,
Here, the initial angular velocity is
and the final angular velocity is
.
The expression change in time is,
Here, the initial time is
and the final time is
.
The expression for angular acceleration is,
(A)
The expression for angular acceleration is,
Substitute 
for
, 
for, 
for
and 
for
.
(B)
The expression for angular acceleration is,
Substitute for, 
for, for and 
for.
(C)
The expression for angular acceleration is,
Substitute 
for, for, 
for and for.
The average angular acceleration between the time interval 
and 
is
.
The average angular acceleration between the time interval and 
is
.
The average angular acceleration between the time interval 
and is
.
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