# Find angular speed

1. Nov 22, 2014

### nesan

1. The problem statement, all variables and given/known data
The propeller blades of an airplane are 4.0 m long. The plane is getting ready for takeoff, and the propeller starts turning from rest at a constant angular acceleration. The propeller blades go through two revolutions between the fifth and the eighth second of the rotation. Find the angular speed at the end of 8.2 s.

3. The attempt at a solution
v = r ω

It seems very easy but I'm stuck on how to find ω

I know there's a constant acceleration

so

ω = ωο + αt

Can someone point me in the right direction with how oto use

"The propeller blades go through two revolutions between the fifth and the eighth second of the rotation."

to get the acceleration.

Than you.

2. Nov 22, 2014

### Orodruin

Staff Emeritus
What is the angular velocity when t = 0, i.e., ωο? Given this, what is the total angle turned as a function of time?

3. Nov 22, 2014

### nesan

Since it says it starts at rest, when t = 0, ωο would be 0?

We use the other formula

θ = ωot + 1/2 αt^2

So θ(t) = 1/2αt^2

How would I figure out α?

4. Nov 22, 2014

### Orodruin

Staff Emeritus
There is some information about $\theta(t)$ given in the problem formulation. Can you decipher it?

5. Nov 22, 2014

### nesan

Whoohoo, I got it.

"The propeller blades go through two revolutions between the fifth and the eighth second of the rotation."

So

θ(8) - θ(5) = 4 PI

- > α (0.5 * 82 - 0.5 * 52) = 4 PI

Solve for α and times it by 8.2 to get angular speed.

I got approximately 5.28 which my text book says is correct. :)

Thank you so much Orodruin.