1) On a certain game show, contestants spin a wheel when it is their turn. One c
ID: 1517451 • Letter: 1
Question
1) On a certain game show, contestants spin a wheel when it is their turn. One contestant gives the wheel an initial angular speed of 3.40 rad/s. The angular acceleration of the wheel is -0.736 rad/s2. Through what angle has the wheel turned when its angular speed is 2.30 rad/s? Give your answer in rad.
2) The angular speed of a propeller on a boat increases with constant acceleration from 13 rad/s to 28 rad/s in 2.0 revolutions. What is the acceleration of the propeller? Give your answer rad/s2.
3) The angular speed of a propeller on a boat increases with constant acceleration from 13 rad/s to 28 rad/s in 2.4 seconds. Through what angle did the propeller turn during this time? Give your answer in rad.
4) A ceiling fan is rotating at 0.80 rev/s . When turned off, it slows uniformly to a stop in 2.0 min. a) How many revolutions does the fan make in this time? please give your answer in rev. b) Using the result from part A, find the number of revolutions the fan must make for its speed to decrease from 0.80 rev/s to 0.40 rev/s. Please give your answer in rev.
Explanation / Answer
1) angular displacement, theta = (wf^2 - wi^2)/(2*alfa)
= (2.3^2 - 3.4^2)/(2*(-0.736)^2)
= 5.79 rad
2) alfa = (wf^2 - wi^2)/(2*theta)
= (28^2 - 13^2)/(2*2*pi)
= 48.9 rad/s^2
3) alfa = (wf - wi)/t
= (28 - 13)/2.4
= 6.25 rad/s^2
theta = wi*t + 0.5*alfa*t^2
= 13*2.4 + 0.5*6.25*2.4^2
= 49.2 rad
4) wi = 0.8*2*pi rad/s = 5.03 rad/s
wf = 0
t = 2 min = 2*60 = 120 s
alfa = (wf - wi)/t
= (0 - 5.03)/(120)
= -0.0419 rad/s^2
theta = (wf^2 - wi^2)/(2*alfa)
= (0^2 - 5.03^2)/(2*(-0.0419))
= 301.92 rad
= 48 revolutions
b) theta = (wf^2 - wi^2)/(2*alfa)
= ((5.03/2)^2 - 5.03^2)/(2*(-0.0419))
= 226.4 rad
= 36 revolutions
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