What is the significance of 2pie in the power formula?

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The significance of 2π in the power formula relates to its role in converting revolutions into linear displacement in circular motion. It represents one complete revolution, equating to approximately 6.28 radians. The formula incorporates force multiplied by this displacement to calculate power. Additionally, the discussion clarifies that the correct terminology should be "distance" rather than "displacement" in this context. Understanding these relationships helps in grasping the connection between linear and angular motion.
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The equation for power is:

F X 2pie X Revolutions

My question is, what is the 2pie for? I know that might seem obvious but I just can't see it.

thanks!
 
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I haven't seen the derivation of the formula, nor ever heard of it before. However, since there are 'revolutions' mentioned, the 2pi would imply that mathematically, the power is dependant somewhat upon circles. Given C=2\pi r
 
I think I figured it out. 2pi = 6.28 radians, which is 1 complete revolution. So in the power formula you have Force X Displacement. To figure out displacement in a circle you take 2pi X the # of revolutions. I get it!
 
Yep that sounds about right. Just be weary about your terminology though. I believe the correct term would be distance rather than displacement in this case.
 
The equations for power are force times linear velocity, or torque times angular velocity.

The relationsips between angular and linear:

force = torque / radius
linear velocity = angular velocity x radius
 

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