Rotational Kinematics? Revolutions of a propeller?

1. Jul 8, 2010

JHCreighton

1. The problem statement, all variables and given/known data
An airplane engine starts from rest; and 2 seconds later, it is rotating with an angular speed of 420 rev/min. If the angular acceleration is constant, how many reovlutions does the propeller undergo during this time?

2. Relevant equations
$$\theta$$ = $$\omega$$ 0 t +1/2 $$\alpha$$ t^2

$$\alpha$$ = $$\Delta$$ $$\omega$$ / $$\Delta$$

3. The attempt at a solution
I thought that if by converting rev/s to rad/s I could use the angular acceleration to somehow find the number of revolutions made in 2 seconds. But I'm not sure if this requires converting, or even if I am on the right track with the angular acceleration.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jul 8, 2010

Ush

1. to do your calculations, you do require converting from rev/m to rad/s
2. what equation relates angular velocity to angular acceleration and time?

3. Jul 8, 2010

JHCreighton

1) So, 420 rev/s would be 840(pi). (I can't find the Pi character) because 1 rev=2(pi) rad. Correct?

2) The equation should be $$\omega$$ = $$\omega$$ 0 + $$\alpha$$ t

4. Jul 8, 2010

Ush

Your question says 420 rev/m (revolutions per minute), not 420rev/s.
you first need to convert 420 rev/m to rev/s

correct,
you are given enough information to calculate angular acceleration.

now, you can use your angular displacement equation to calculate the number of radians rotated in 2 seconds.

you can then convert radians to revolutions.

5. Jul 8, 2010

JHCreighton

OK, so let's see. 420 rev/MIN is 7 rev/s, which is 44 rad/s. Rearranging the kinematic equation to be $$\alpha$$ = vf /t and substituting, I get the angular acceleration to be 22 rad/s^2. Then, if the initial velocity is 0 rad/s, the final velocity is again 44 rad/s. This converted to rev/s is 44/2(pi), which equals 7 revolutions. I think I took the long way around to get here, but does this seem like the correct process? Or at least it lead to the correct answer?

6. Jul 8, 2010

Ush

after you find your angular acceleration, (22rad/s^2). You need to find your angular displacement. (Remember, angular displacement is the number of radians the propeller turns)

so no, 7 revolutions is not the correct answer.

7. Jul 8, 2010

JHCreighton

Jeez, this problem has just worked me over, and for no good reason. OK, simply substituting everything into the angular displacement equation, then converting back to revolutions, I get 14 rev. I can't tell you how much I appreciate the help, especially since you took the time to go step by step with me, without just tossing out everything I needed at once.
My sincerest thanks,
JHCreighton

8. Jul 8, 2010

Ush

sorry, 7 revolutions was the correct answer. I didn't do the math, I just looked at what you were saying.. But if you do the math
--
wf^2 = wi^2 + 2⍺θ
rearrange for θ

OR

θf = θi + Wit + ½⍺t^2
rearrange for θ
--

θ turns out to be 44radians = 7 revolutions =p