Calculating Flywheel Rotations in Angular Speed and Constant Acceleration

[Arman777]

Homework Statement

[/B] A flywheel with a D=1.2m is rotating at an angular speed of 200 rev/min
(a) Whats the angular speed in rad/s ?
(b)Whats v=? in the point on the rim ?
(c)What const. ∝ ( in rev/min^2) will increase its angular speed to 1000 rev/min in 60 sec ?
(d)How many revolutions does the wheel make during that 60 sec ?

2. Homework Equations
Rotational Kinematics Equations

The Attempt at a Solution

[/B] I found a,b,c correctly (for long tries ) but I stucked at d.

I guess I ll use here $Δθ=wt-1/2∝t^2$

(a) w=20.9 rad/s
(b)v=12.5
(c)=800 rev/min^2

Now for d,

lets to write all equaiton in rev/min form so
20.9rad/sec=20.9.2π.60=7879 rev/min
I don't know what will be the left part cause Δθ in units its normally just rev I guess so
θ-200rev/min=7879rev/min.1min+1/2 (800rev/min^2).(1 min)^2
Here I get a huge number...

Thank you

 

[mfb]

20.9rad/sec=20.9.2π.60=7879 rev/min

You established before that 200 rev/min corresponds to 20.9 rad/s (which is correct). How can it correspond to a larger number of revolutions per minute now?

θ-200rev/min

You cannot subtract an angle and an angular velocity. That's like adding 3 meters to 1 minute: It does not make sense.

You can use the formula you posted, but it is probably easier to find the average angular velocity (in rev/min) and to use that.

 

[Arman777]

You cannot subtract an angle and an angular velocity. That's like adding 3 meters to 1 minute: It does not make sense.

ohh I see...so I can convert 200rev/min to rev which its just 200 or ..I don't know ?

 

[mfb]

You cannot "convert an angular velocity to revolutions" in the same way you cannot convert apples to minutes. There is no need for such a conversion. Your formula multiplies the angular velocity by a time. The product of those two is a number of revolutions or an angle, depending on which units you use.

 

[Arman777]

ok then how can I found inital rev ? If other parts are correct ?

 

[Arman777]

Your formula multiplies the angular velocity by a time. The product of those two is a number of revolutions or an angle, depending on which units you use.

oh I see...

 

[Arman777]

Here my new try
Δθ=20.9 rad/s.60s-1/2.(0.035 rad/sec^2).(60sec)^2
Δθ=1317rad

 

[mfb]

Your angular acceleration seems to be too low.

 

[Arman777]

Your angular acceleration seems to be too low.

yeah,sorry it would be 1.40 rad/sec ?

 

[Arman777]

I found yeyyyyy

 

[Arman777]

Thanks