What is the formula for calculating RPMs of a flywheel with external force?

[Pinon1977]

I have a question. I have a flywheel that is 108' is diameter and it weights approximately 1600 lbs. It has an external force of 600lbs acting upon it at 90* to the axel. Like a water wheel. How can i determine the RPMs that my flywheel will turn with this type of force being applied to the flywheel? Would you take the 600 pounds x the rate of gravity 9.8 m/s^2? Thanks in advance

 

[Nugatory]

How can i determine the RPMs that my flywheel will turn with this type of force being applied to the flywheel? Would you take the 600 pounds x the rate of gravity 9.8 m/s^2? Thanks in advance

That's not how you would calculate the effect of the force on the wheel - you'll need the moment of inertia of the wheel and the magnitude of the torque from the force, which depends on how far from the axle the force is applied. Google for "torque moment of inertia" if you are not familiar with these concepts; you'll also find them in any college-level first-year physics textbook.

However, there is another difficulty in this problem as you've stated it. You haven't considered the friction acting on the wheel, either from air resistance or at the pivot. Without friction, the wheel will keep on speeding up as long as the torque is acting on it; there's no particular RPM at which it will stabilize.

 

[Pinon1977]

Thank you for the feedback. The flywheel is resting on electromagnetic bearing so there's no friction coefficient to take into consideration. As far as the driving force of the 600 pounds. Think of it as a Constant feed of 600 pounds being applied to the flywheel, much like a water wheel does with water. The driving force in this particular situation I can't explain in great detail, but the closest thing I can equate it to would be like 600 pounds of water hitting a water wheel at a continuous rate. I'm just trying to figure out how the 600 pounds of force acting upon the flywheel will affect the RPMs.

 

[Nugatory]

Think of it as a Constant feed of 600 pounds being applied to the flywheel, much like a water wheel does with water.

A water wheel doesn't experience a constant force from the water. The torque is at full strength when the wheel is not rotating, becomes smaller as the wheel spins up, and reaches zero when the the rim of the wheel is moving at the same speed as the water. Once the torque reaches zero the wheel stops accelerating and remains at whatever speed that is. That's a different problem than the one you originally described.

 

[Dale]

If there is no dissipation then it will turn as fast as the water hitting it. The weight of the water will not change the final speed, but it will influence how fast it gets up to speed.

 

[Pinon1977]

Please see drawing. What you're saying is the RPMs will continue to increase infinitely? The 600 lbs of force has got to level out at some RPM I would think?

 

[Nugatory]

Please see drawing. What you're saying is the RPMs will continue to increase infinitely? The 600 lbs of force has got to level out at some RPM I would think?

We are saying that if the force gets smaller and levels out at zero (if there were friction, levels out at whatever non-zero value is needed to overcome that friction) the RPMs will not increase infinitely.

The confusion arises because in your original problem statement you specified a constant force of 600 pounds, not a force that might get smaller as the wheel speeds up.

 

[TurtleMeister]

Think of it as a Constant feed of 600 pounds being applied to the flywheel, much like a water wheel does with water.

The 600 pounds has nothing to do with the final RPM of your wheel (if it is like a water wheel as you stated). Remember the universality of free fall? All bodies fall at the same rate regardless of their mass. As Dale stated, the weight will only have an effect on how much time it takes for the wheel to reach that final RPM. What will affect the final RPM is the diameter of the wheel.

 

[Pinon1977]

Ok. That being said, "What will affect the final RPM is the diameter of the wheel.", The flywheel diameter is 102" and weighs 1600 lbs. So given that info how would you derive the RPMs.

 

[Pinon1977]

Consequently, thank you for being patient with me. It's greatly appreciated you guys are always a bunch of help!

 

[TurtleMeister]

Ok. That being said, "What will affect the final RPM is the diameter of the wheel.", The flywheel diameter is 102" and weighs 1600 lbs. So given that info how would you derive the RPMs.

The weight of the wheel will have little or no affect on it's RPM. However, the weight of the falling body and the weight of the wheel will affect how long it takes the wheel to reach it's maximum RPM.

How fast will the falling body be traveling when it makes contact with the wheel? You already know about the 9.8 m/s^2, so you should be able to calculate that.

When the wheel reaches it's maximum speed, the wheel's circumference will be traveling at the same speed as the falling body (minus friction losses). You already know the wheel's diameter, so now you need to calculate it's circumference.

When you know those two things (speed of falling body and circumference of the wheel), you should be able to calculate it's RPM by simple division.

 

[Pinon1977]

Now that's the clue I was looking for, sir. Thank you. Ok, so I am going to throw around a few equations and I will post the result. Thanks again, guys and gals.

 

[rootone]

Now that's the clue I was looking for, sir. Thank you. Ok, so I am going to throw around a few equations and I will post the result. Thanks again, guys and gals.

Have fun, and if the actual result don't look like what you expected, I am sure somebody here will be able to help figure it out.