Convert to Radians per Second

$65 \frac{rev}{\min}$

Step 1

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

$\frac{65 \cdot round}{min} \cdot \frac{2 π \cdot radian}{round} \cdot \frac{min}{60 \cdot sec}$

Step 2

Cancel the common units.

$\frac{65 \cdot round}{min} \cdot \frac{2 π \cdot radian}{round} \cdot \frac{min}{60 \cdot sec}$

Step 3

Simplify the expression to find the solution in $\frac{radian}{sec}$ .

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Step 3.1

Cancel the common factor of $65$ and $60$ .

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Step 3.1.1

Factor $5$ out of $65 \cdot (2 π)$ .

$\frac{5 (13 \cdot (2 π))}{60} \cdot \frac{radian}{sec}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $5$ out of $60$ .

$\frac{5 (13 \cdot (2 π))}{5 (12)} \cdot \frac{radian}{sec}$

Step 3.1.2.2

Cancel the common factor.

$\frac{5 (13 \cdot (2 π))}{5 \cdot 12} \cdot \frac{radian}{sec}$

Step 3.1.2.3

Rewrite the expression.

$\frac{13 \cdot (2 π)}{12} \cdot \frac{radian}{sec}$

Step 3.2

Cancel the common factor of $2$ and $12$ .

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Step 3.2.1

Factor $2$ out of $13 \cdot (2 π)$ .

$\frac{2 (13 \cdot (π))}{12} \cdot \frac{radian}{sec}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $2$ out of $12$ .

$\frac{2 (13 \cdot (π))}{2 \cdot 6} \cdot \frac{radian}{sec}$

Step 3.2.2.2

Cancel the common factor.

$\frac{2 (13 \cdot (π))}{2 \cdot 6} \cdot \frac{radian}{sec}$

Step 3.2.2.3

Rewrite the expression.

$\frac{13 \cdot (π)}{6} \cdot \frac{radian}{sec}$

$\frac{13 π}{6} \cdot \frac{radian}{sec}$

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Convert to Radians per Second

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