How Long Does It Take for a Flywheel to Stop?

[Arman777]

Homework Statement

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.

Homework Equations

$w-w_0=∝t$

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 couldn't found

 

[TomHart]

40=1.5t-1/2∝t^2
but I couldn't found

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.

 

[BvU]

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

 

[Arman777]

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

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

 

[ehild]

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

 

[Arman777]

What is the turning angle when the flywheel rotates 40 times?

turning angle ?

 

[ehild]

turning angle ?

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

 

[Arman777]

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

2π ?

 

[Arman777]

Are we turning 40 rev to 80π rad ??

 

[ehild]

2π ?

yes. And during 40 revolutions?

 

[Arman777]

yes. And during 40 revolutions?

I posted 80π ?

 

[ehild]

I posted 80π ?

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

 

[Arman777]

$w-w_0=∝t$and
$Δθ=wt$

or $Δθ=wt-\frac 1 2∝t^2$

 

[ehild]

$w-w_0=∝t$and
$Δθ=wt$

or $Δθ=wt-\frac 1 2∝t^2$

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.

 

[Arman777]

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

 

[Arman777]

https://www.physicsforums.com/threads/rotationel-motion.902930/

 

[Arman777]

Δw=-1.5 and Δθ is 80 so

Δw=-1.5=∝t and

80=1.5t-1/21.5t

Is this true ?

 

[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 = v_o + at → ω = ω_o + αt
v² = v_o² + 2ax → ω² = ω_o² + 2αθ
x = v_ot + at²/2 → θ = ω_ot + αt²/2
F = ma → Γ = Iα
ρ = mv → L = Iω
E_k = mv²/2 → E_k = Iω²/2

80=1.5t-1/21.5t

Is this true ?

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

 

[Arman777]

Ok,I found...Thanks all of you...Just couldn't see that