Convert cycle / square minute to revolution / square second

Learn how to convert 1 cycle / square minute to revolution / square second step by step.

Calculation Breakdown

Set up the equation

1.0 (\frac{c y c l e}{s q u a r e m i n u t e}) = x (\frac{r e v o l u t i o n}{s q u a r e s e c o n d})

Define the base values of the selected units in relation to the SI unit

(\frac{r a d i a n}{s q u a r e s e c o n d})

Left side: 1.0 (\frac{c y c l e}{s q u a r e m i n u t e}) = \frac{π}{1.8 \times 10^{3}} (\frac{r a d i a n}{s q u a r e s e c o n d}) = \frac{π}{1.8 \times 10^{3}} (\frac{r a d}{s^{2}})

Right side: 1.0 (\frac{r e v o l u t i o n}{s q u a r e s e c o n d}) = 2.0 \times π (\frac{r a d i a n}{s q u a r e s e c o n d}) = 2.0 \times π (\frac{r a d}{s^{2}})

Insert known values into the conversion equation to determine

x

1.0 (\frac{c y c l e}{s q u a r e m i n u t e}) = x (\frac{r e v o l u t i o n}{s q u a r e s e c o n d})

Insert known values =>

1.0 \times \frac{π}{1.8 \times 10^{3}} \times (\frac{r a d i a n}{s q u a r e s e c o n d}) = x \times 2.0 \times π \times (\frac{r a d i a n}{s q u a r e s e c o n d})

Or

1.0 \cdot \frac{π}{1.8 \times 10^{3}} \cdot (\frac{r a d}{s^{2}}) = x \cdot 2.0 \times π \cdot (\frac{r a d}{s^{2}})

Cancel SI units

1.0 \times \frac{π}{1.8 \times 10^{3}} \cdot (\frac{r a d}{s^{2}}) = x \times 2.0 \times π \times (\frac{r a d}{s^{2}})

Conversion Equation

\frac{π}{1.8 \times 10^{3}} = x \times 2.0 \times π

Cancel factors on both sides

Cancel factors

\frac{π}{1.8 \times 10^{3}} = x \times π \times 2.0

Simplify

\frac{1.0}{1.8 \times 10^{3}} = x \times 2.0

Switch sides

x \times 2.0 = \frac{1.0}{1.8 \times 10^{3}}

Isolate

x

Multiply both sides by

(\frac{1.0}{2.0})

x \times 2.0 \times \frac{1.0}{2.0} = \frac{1.0}{1.8 \times 10^{3}} \times \frac{1.0}{2.0}

Cancel

x \times 2.0 \times \frac{1.0}{2.0} = \frac{1.0 \times 1.0}{1.8 \times 10^{3} \times 2.0}

Simplify

x = \frac{1.0}{1.8 \times 10^{3} \times 2.0}

Rewrite equation

\frac{1.0}{10^{3}} can be rewritten to 10^{- 3}

Rewrite

x = \frac{10^{- 3}}{1.8 \times 2.0}

Solve

x

x \approx 0.0002777778 \approx 2.7778 \times 10^{- 4}

Conversion Equation

1.0 (\frac{c y c l e}{s q u a r e m i n u t e}) \approx 2.7778 \times 10^{- 4} (\frac{r e v o l u t i o n}{s q u a r e s e c o n d})

View All Examples