# Flywheel Rotation Question

1. Feb 6, 2017

### Arman777

1. The problem statement, all variables and given/known data
A flywheel turns through 40 rev as it slows from an angular speed of 1.5 rad/s to a stop.Assuming a constant acceleration,find the tme for it to come to rest.

2. Relevant equations
$w-w_0=∝t$

3. The attempt at a solution
In Δt secon the change in w will be 1.5 and this time it will rotate 40 times..I tried every equaiton like
0-1.5=∝t
or
40=1.5t-1/2∝t^2
but I couldnt found

2. Feb 6, 2017

### TomHart

There is another equation that you should know that involves initial and final velocities, acceleration and angle of rotation.
Also, you are mixing units here: revolutions and radians.

3. Feb 6, 2017

### BvU

Check the units of your last equation (I wonder: why couldn't you solve it ? - or did it just give the wrong answer ?)

4. Feb 6, 2017

### Arman777

I am really bad at this whole rotation-torque subject.I ll look again..I know my equation is wrong...

5. Feb 6, 2017

### ehild

What is the turning angle when the flywheel rotates 40 times?
Also check the signs.

6. Feb 6, 2017

### Arman777

turning angle ?

7. Feb 6, 2017

### ehild

Or angle of rotation. What is the angle the wheel rotates during one revolution?

8. Feb 6, 2017

2π ?

9. Feb 6, 2017

### Arman777

Are we turning 40 rev to 80π rad ??

10. Feb 6, 2017

### ehild

yes. And during 40 revolutions?

11. Feb 6, 2017

### Arman777

I posted 80π ?

12. Feb 6, 2017

### ehild

Yes. So what are the equations for the change of angular velocity and angular rotation angle in time Δt?

13. Feb 6, 2017

### Arman777

$w-w_0=∝t$and
$Δθ=wt$

or $Δθ=wt-\frac 1 2∝t^2$

14. Feb 6, 2017

### ehild

Δθ=wt is only valid for constant angular velocity.
$Δθ=w_0t+\frac {1 }{2}\alpha t^2$ that is valid with positive sign.
Eliminate alpha.

Last edited: Feb 6, 2017
15. Feb 6, 2017

### Arman777

I guess I have to study this more to understand the basics.I ll open another thread

16. Feb 6, 2017

### Arman777

17. Feb 6, 2017

### Arman777

Δw=-1.5 and Δθ is 80 so

Δw=-1.5=∝t and

80=1.5t-1/21.5t

Is this true ?

18. Feb 6, 2017

### TomHart

The rotational equations pretty much follow directly from the linear equations. So if you can remember the linear equations, the rotational should be easy.
v = vo + at → ω = ωo + αt
v2 = vo2 + 2ax → ω2 = ωo2 + 2αθ
x = vot + at2/2 → θ = ωot + αt2/2
F = ma → Γ = Iα
ρ = mv → L = Iω
Ek = mv2/2 → Ek = Iω2/2

I think so, except it should be 80π instead of 80.

19. Feb 6, 2017

### Arman777

Ok,I found....Thanks all of you...Just couldnt see that