Practice 7B: | 1 | 2 | 3 | 4 |Go up
Angular Speed  - by Matt Henderson, 2003

1. A car tire rotates with an average angular speed of 29 rad/s. In what time interval will the tire rotate 3.5 times?

Here's what you know, wavg = 29 rad/s and Dq = (3.5)(2p) = 7pie rad 1 time around the circle = 2p

Now use the formula wavg = Dq/Dt to find the time 29= 7p/Dt and Dt = .76 s

2. A girl ties a toy airplane to the end of a string and swings it around her head. the plan's average angular speed is 2.2 rad/s. In what time interval will the plane move through an angular displacement of 3.3 rad?

Here's what you know, wavg = 2.2 rad/s and Dq = 3.3 rad

Now use the formula wavg = Dq/Dt to find the time 2.2= 3.3/Dt and Dt = 1.5 s

3. The average angular speed of a fly moving in a circle is 7.0 rad/s. How long does the fly take to move through 2.3 rad??

Here's what you know, wavg = 7.0 rad/s and Dq = 2.3 rad

Now use the formula wavg = Dq/Dt to find the time 7.0= 2.3/Dt and Dt = .33 s

4. Fill in the unknown quantities in the following table

First 1 rev/s = 2p rad/s and 1 rev is the same as 1 time around the circle

wavg                                         Dq                                                    Dt

a.     ?                                            2.3 rad                                                10 s

b.    .75 rev/s                                        ?                                                   .050 s

c.     ?                                            -1.2 turns                                               1.2 s

a. use the formula wavg = Dq/Dt to find the angular speed  wavg= 2.3/10 and wavg = .23 rad/s

b. 1 rev/s = 2pie rad/s so (.75)(2p) = 4.712

use the formula wavg = Dq/Dt to find the arc length  4.712= Dq/.05 and Dq = .2356 rad

c. 1 turn = 2p so (-1.2)(2p)= -7.5398 rad

use the formula wavg = Dq/Dt to find the angular speed  wavg= -7.539/1.2 and wavg = -6.28 rad/s

d.  use the formula wavg = Dq/Dt to find the time 2p= 1.5p/Dt and Dt = .75 s