Practice 7D: | 1 | 2 |
3 | 4 | 5 |
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**Angular kinematics - **by Matt Henderson, 2003

**1. What is the angular acceleration of the upside-down
bicycle wheel in Sample Problem 7D if it rotates through 18.0 rad in 5.00 s? **

w_{f}= 18.0rad and w_{i}=14.8 rad and t = 5.0s, so use the equation w_{f}= w_{i}+ a(Dt)

18 = 14.8 + (a) 5 a = .64 rad/s^2

**2. A diver performing a double somersault spins at an
angular speed of 4.0p
rad/s precisely 0.50s after leaving the platform. Assuming the diver begins with
zero initial angular speed and accelerates at a constant rate, what is the
diver's angular acceleration during the double somersault? **

w_{f}= 4.0prad/s and w_{i}=0 and t = .50s, so the Dw = 4.0p rad/s

now use the formula a_{avg}= Dw/Dt

a_{avg = }4.0p/.5 a_{avg = 25.13 rad/s^2}

**3.** **A fish swimming behind an ail tanker gets
caught in a whirlpool created by the ship's propellers. The fish has an angular
speed of 1.0 rad/s After 4.5s, the fish's angular speed is 14.5 rad/s. If the
water in the whirlpool accelerates at a constant rate, what is the angular
acceleration? **

w_{f}= 14.5rad/s and w_{i}=1 rad/s and t = 4.5 s, so use the equation w_{f}= w_{i}+ a(Dt)

14.5 = 1 + (a) 4.5 a = 3 rad/s^2

**4. A remote-controlled car's wheel accelerates at 22.4
rad/s^2. If the wheel begins with an angular speed of 10.8 rad/s, what is the
wheel's angular speed after exactly three full turns?**

a = 22.4 rad/s^2 and w_{i}=10.8 rad/s and t = 3 rev since q= (2p)(t) q = (2p)(3) = 18.5 rad

we use the formula a = ( w^2 -w0^2)/(2*p)

22.4 = (w_{f}^2 - 10.8^2)/(2* 18.5) solve use algebraic skills and you will find that

w_{f}= 31 rad/s

**5. How long does the wheel in item 4 take to make the
three turns? **

use the formula w_{f}= w_{i}+ a(Dt) to find (t)a = 22.4 rad/s^2 andw_{f}= 31 rad/s and w_{i}=10.8 rad/s so we just plug it in.

31 = 10.8 + 22.4(t) and t = .9 s