Precalculus Examples

$60 r p m$

Use the fact that each revolution is $2 π$ radians and each minute is $60$ seconds to convert from $rpm$ to $\frac{radian}{sec}$

$\frac{60 \cdot round}{min} \cdot \frac{2 π \cdot radian}{round} \cdot \frac{min}{60 \cdot sec}$

Cancel the common units.

$\frac{60 \cdot round}{min} \cdot \frac{2 π \cdot radian}{round} \cdot \frac{min}{60 \cdot sec}$

Cancel the common factor of $60$ .

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Cancel the common factor.

$\frac{60 \cdot (2 π)}{60} \cdot \frac{radian}{sec}$

Divide $2 π$ by $1$ .

$2 π \frac{radian}{sec}$

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