Finding time using a given torque, etc.

[aligass2004]

Homework Statement

Flywheels are large, massive wheels used to store energy. They can be spun up slowly, then the wheel's energy can be released quickly to accomplish a task that demands high power. An industrial flywheel has a 1.2m diameter and a mass of 250kg. A motor spins up the flywheel with a constant torque of 40Nm. How long does it take the flywheel to reach top angular speed of 1250rpm?

Homework Equations

Wf = Wi + alpha(delta t)

The Attempt at a Solution

I tried using the above equation except I substituted delta W/delta t for alpha. I got 2815.315s, but that seems awfully high, and it wasn't right.

 

[hage567]

I don't see how you would have got that to work. Did you use the information about torque? Do you know how to find the moment of inertia of a disk? You can find the angular acceleration using those two quantities. Once you've done that, use the equation under "relevant equations" to find the time.

 

[aligass2004]

I = m(r^2) = 250(.6^2) = 90. I did that and I got the exact same answer.

 

[aligass2004]

I'm still unsure about this problem.

 

[hage567]

Remember that torque = I * alpha. You found I, you were given the torque in the question. So you can get alpha.

Also, a flywheel is shaped like a disk, so for I you should use 0.5*M*R^2, not just M*R^2.

 

[aligass2004]

Ok, using the new I = 45, alpha = .889. So then substituting into Wf = Wi + alpha (delta time), delta time = 1406.074. Does that sound right?

 

[hage567]

Your angular velocity was expressed as 1250 rpm, (revolutions per minute). You need to change that to radians/second, so you units are consistent and correct. Do you know how to do that?

 

[aligass2004]

Why no I do not...I know how to change it to revolutions/second, but not radians/second

 

[hage567]

There are 2*pi radians per revolution.

 

[aligass2004]

Do I change revolutions/minute to revolutions/second then then do the 2pi radians?

 

[hage567]

Yes, you must do both.

 

[aligass2004]

Got it. Thanks!