How much Torque and Speed Are in a Horsepower (or Watts)?

Let's take a look at how torque and speed are related to power:

Suppose we take a breaker bar one foot long, and use it to turn a bolt exactly one turn.

Horsepower torque calculation
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How are did the end of the breaker bar travel? Well it travelled the circumference of the circle.

So we recall that the circumference of a circle equals the value Pi multiplied by the diameter. And we recall that the diameter is double the radius. The radius of our circle is one foot, since the breaker bar was one foot long.

So C = (2)(Pi)(r) = (2)(Pi)(1 foot) = (2)(Pi) feet

The value for Pi is roughly 3.14159, so (2)(Pi) feet is approximately 6.28 feet.

Now let's also suppose it takes a constant one pound of force to rotate the breaker bar (note: we'll also assume the breaker bar has zero mass, so we don't have to worry about effects of gravity, and the applied force is in the same plane as the rotation, and the applied force is exactly 12 inches from the center of the bolt.)

Let's also suppose it took us one second to rotate the breaker bar that one revolution.

So the power used in rotating our breaker bar calculates as such:

P = [1 pound] * [(2)(Pi) feet] / [1 second] = (2)(Pi) pound-feet per second.

We also know that one horsepower is equivalent to raising 550 pounds one foot in one second. Or stated differently, one horsepower is 550 pound-feet per second.

Now, let's consider how much torque we would need to apply to develop one horsepower:

[550 lb-feet/second] / [(2)(pi) lb-feet/second] = 275/Pi

So we would need roughly 275/3.14159 or 87.5 times the torque or speed we applied to generate one horsepower.

And we know that there are 60 revolutions per minute for every revolution per second.

So 1 HP = [torque]*[revolutions per minute] / [(60)(275/Pi)]

Now the same calculation could be done using Metric SI units, so that the force is in Newtons, the speed is in radians per second (or minute), and the power is in Watts.