Practice 7D: | 1 | 2 | 3 | 4 | 5 | Go up
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 = 18.0 rad 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

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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 = 4.0p rad/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}

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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 = 14.5 rad/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

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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

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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 and  w_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 

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