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?

wf = 18.0 rad and wi  = 14.8 rad and t = 5.0s, so use the equation wf = wi + 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?

wf = 4.0p rad/s and wi  = 0 and t = .50s, so the Dw = 4.0p rad/s

now use the formula aavg = Dw/Dt
aavg =  4.0p/.5        aavg = 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?

wf = 14.5 rad/s and wi  = 1 rad/s and t = 4.5 s, so use the equation wf = wi + 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 wi  = 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 = (wf^2 - 10.8^2)/(2* 18.5) solve use algebraic skills and you will find that