# Flywheel Rotation Question

Gold Member

## 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.

##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 couldnt found

40=1.5t-1/2∝t^2
but I couldnt 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
Homework Helper
Check the units of your last equation (I wonder: why couldn't you solve it ? - or did it just give the wrong answer ?)

Gold Member
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
Homework Helper
What is the turning angle when the flywheel rotates 40 times?
Also check the signs.

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

ehild
Homework Helper
turning angle ?
Or angle of rotation. What is the angle the wheel rotates during one revolution?

Gold Member
Or angle of rotation. What is the angle the wheel rotates during one revolution?
2π ?

Gold Member
Are we turning 40 rev to 80π rad ??

ehild
Homework Helper
2π ?
yes. And during 40 revolutions?

Gold Member
yes. And during 40 revolutions?
I posted 80π ?

ehild
Homework Helper
I posted 80π ?
Yes. So what are the equations for the change of angular velocity and angular rotation angle in time Δt?

Gold Member
##w-w_0=∝t##and
##Δθ=wt ##

or ##Δθ=wt-\frac 1 2∝t^2##

ehild
Homework Helper
##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.

Last edited:
Gold Member
I guess I have to study this more to understand the basics.I ll open another thread

Gold Member
Gold Member
Δw=-1.5 and Δθ is 80 so

Δw=-1.5=∝t and

80=1.5t-1/21.5t

Is this true ?

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

80=1.5t-1/21.5t

Is this true ?
I think so, except it should be 80π instead of 80.

Arman777
Gold Member
Ok,I found....Thanks all of you...Just couldnt see that

TomHart