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Cruiser
Posts: 129
Coastal , NJ | By the definition of torque: torque=force × radius. We can rearrange this to determine force=torque ÷ radius. These two values can be substituted into the definition of power:
\mbox{power} = \frac{\mbox{force} \times \mbox{linear distance}}{\mbox{time}}=\frac{\left(\frac{\mbox{torque}}{r}\right) \times (r \times \mbox{angular speed} \times t)} {t} = \mbox{torque} \times \mbox{angular speed}.
The radius r and time t have dropped out of the equation. However angular speed must be in radians, by the assumed direct relationship between linear speed and angular speed at the beginning of the derivation. If the rotational speed is measured in revolutions per unit of time, the linear speed and distance are increased proportionately by 2π in the above derivation to give:
\mbox{power}=\mbox{torque} \times 2 \pi \times \mbox{rotational speed}. \,
If torque is in lbf·ft and rotational speed in revolutions per minute, the above equation gives power in ft·lbf/min. The horsepower form of the equation is then derived by applying the conversion factor 33,000 ft·lbf/min per horsepower:
\mbox{power} = \mbox{torque } \times\ 2 \pi\ \times \mbox{ rotational speed} \cdot \frac{\mbox{ft}\cdot\mbox{lbf}}{\mbox{min}} \times \frac{\mbox{horsepower}}{33000 \cdot \frac{\mbox{ft }\cdot\mbox{ lbf}}{\mbox{min}} } \approx \frac {\mbox{torque} \times \mbox{RPM}}{5252}
because 5252.113122... = \frac {33,000} {2 \pi}. \,
[edit] Principle of Moments
The Principle of Moments, also known as Varignon's theorem (not to be confused with the geometrical theorem of the same name) states that the sum of torques due to several forces applied to a single point is equal to the torque due to the sum (resultant) of the forces. Mathematically, this follows from:
(\mathbf{r}\times\mathbf{F}_1) + (\mathbf{r}\times\mathbf{F}_2) + \cdots = \mathbf{r}\times(\mathbf{F}_1+\mathbf{F}_2 + \cdots). | |
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Cruiser
Posts: 64
Ma. | I agree | |
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Cruiser
Posts: 235
Kincardine, Ontario, Canada | I had it explained easier.
Holding back a fart is torque
letting it go is HP
Kinda puts it all in perspective | |
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Visionary
Posts: 2118
Pitt Meadows, BC Canada | WHOA! There is a fault in the formula....
It should be:
(\mathbf{r}\times\mathbf{F}_1) + (\mathbf{r}\times\mathbf{F}_2) + \idiots = \mathbf{r}\times(\mathbf{F}_1+\mathbf{F}_2 + \idiots).
And I agree with my fellow Canuck - MORE TORQUE=LESS SUCK | |
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Tourer
Posts: 354
20 miles west of Chicago. | Now my mind is boggled. Well, it was already a little boggled, but now it's almost totally boggled. I'm going to walk over to the bar, a distance of 18 ft., (I hope I can make it without, walking into a wall, what with my mind all boggled..) and pour myself about four fingers of Eagle Rare or W.L. Weller, add a splash of branch water, and give it a think. I hope that within an hour so I can get sufficiently de-boggled (un-boggled?..) to find my way upstairs. By then I should be a little torqued myself.
Edited by Mudge 2009-03-01 9:47 PM
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Visionary
Posts: 8144
New Bohemia, VA | we got a hefty snow here in central va but missed this discussion due to more pressing issues. I don't know if this applies, but my wife has a theory about power. Here goes: Given two cars, one with a bigger engine than the other, will travel faster at the same speed than the car with the smaller engine. To explain. Take a Chevy Tahoe, not that I like Chevy's or Tahoe's, so therefore you can take it. But back to the point, take a Chevy Tahoe and a Ford Pinto traveling down I-95, both at exactly 55 mph, the Tahoe will be moving faster. That is what I call her theory of relativity. Okay, something to ponder if you're stuck in the snow, I'm at work because I have internet access here and not at home, otherwise I'd be working from home. We got about 6 to 10 inches of the white stuff around Richmond. | |
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Thoughts on torque for a snowy Northeast night...