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

In summary, the equation for power is force times linear velocity or torque times angular velocity. The 2pi in the equation represents a full revolution in radians, and is used to calculate displacement in a circular motion. The relationships between angular and linear quantities are force = torque / radius and linear velocity = angular velocity x radius.
  • #1
shayrgob
13
1
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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  • #2
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 [tex]C=2\pi r[/tex]
 
  • #3
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!
 
  • #4
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.
 
  • #5
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
 

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

What is the power formula?

The power formula is a mathematical equation that calculates the amount of power generated or used by a system. It is represented as P = W/t, where P is power, W is work, and t is time.

How is power different from energy?

Power and energy are related but have different meanings. Power is the rate at which energy is generated or consumed, while energy is the total amount of work done or heat transferred. In other words, power is the speed at which energy is being used.

Can the power formula be used for both mechanical and electrical systems?

Yes, the power formula can be applied to both mechanical and electrical systems as long as the units of work and time are consistent. For mechanical systems, work is typically measured in joules and time in seconds, while for electrical systems, work is measured in watts and time in hours.

How is the power formula used in real life?

The power formula is commonly used in various fields such as engineering, physics, and economics. It is used to calculate the power output of machines, determine the efficiency of systems, and analyze energy usage and costs.

What are some common units used for power?

The most common units used for power are watts (W), kilowatts (kW), and horsepower (hp). In the metric system, watts and kilowatts are used, while horsepower is more commonly used in the imperial system. Other units such as BTU/second and foot-pounds per minute may also be used in specific contexts.

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