Practice 7B: | 1 | 2 |
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**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, w

_{avg}= 29 rad/s and Dq = (3.5)(2p) = 7pie rad 1 time around the circle = 2pNow use the formula w

_{avg}= Dq/Dt to find the time 29= 7p/Dt and Dt = .76 s

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**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, w

_{avg}= 2.2 rad/s and Dq = 3.3 radNow use the formula w

_{avg}= 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,
w_{avg} =
7.0 rad/s and Dq
= 2.3 rad

Now use the
formula w_{avg}
= 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

w

_{avg}Dq Dta. ? 2.3 rad 10 s

b. .75 rev/s ? .050 s

c. ? -1.2 turns 1.2 s

d. 2pie rad 1.5pie rad ?

a. use the formula w

_{avg}= Dq/Dt to find the angular speed w_{avg}= 2.3/10 and w_{avg}= .23 rad/sb. 1 rev/s = 2pie rad/s so (.75)(2p) = 4.712

use the formula w

_{avg}= Dq/Dt to find the arc length 4.712= Dq/.05 and Dq = .2356 radc. 1 turn = 2p so (-1.2)(2p)= -7.5398 rad

use the formula w

_{avg}= Dq/Dt to find the angular speed w_{avg}= -7.539/1.2 and w_{avg}= -6.28 rad/sd. use the formula w

_{avg}= Dq/Dt to find the time 2p= 1.5p/Dt and Dt = .75 s

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