Convert radian / (minute • second) to cycle / square minute

Learn how to convert 1 radian / (minute • second) to cycle / square minute step by step.

Calculation Breakdown

Set up the equation

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

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{r a d i a n}{m i n u t e \times s e c o n d}) = \frac{1.0}{60.0} (\frac{r a d i a n}{s q u a r e s e c o n d}) = \frac{1.0}{60.0} (\frac{r a d}{s^{2}})

Right 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}})

Insert known values into the conversion equation to determine

x

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

Insert known values =>

1.0 \times \frac{1.0}{60.0} \times (\frac{r a d i a n}{s q u a r e s e c o n d}) = x \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})

Or

1.0 \cdot \frac{1.0}{60.0} \cdot (\frac{r a d}{s^{2}}) = x \cdot \frac{π}{1.8 \times 10^{3}} \cdot (\frac{r a d}{s^{2}})

Cancel SI units

1.0 \times \frac{1.0}{60.0} \cdot (\frac{r a d}{s^{2}}) = x \times \frac{π}{1.8 \times 10^{3}} \times (\frac{r a d}{s^{2}})

Conversion Equation

\frac{1.0}{60.0} = x \times \frac{π}{1.8 \times 10^{3}}

Switch sides

x \times \frac{π}{1.8 \times 10^{3}} = \frac{1.0}{60.0}

Isolate

x

Multiply both sides by

(\frac{1.8 \times 10^{3}}{π})

x \times \frac{π}{1.8 \times 10^{3}} \times \frac{1.8 \times 10^{3}}{π} = \frac{1.0}{60.0} \times \frac{1.8 \times 10^{3}}{π}

Cancel

x \times \frac{π \times 1.8 \times 10^{3}}{1.8 \times 10^{3} \times π} = \frac{1.0 \times 1.8 \times 10^{3}}{60.0 \times π}

Simplify

x = \frac{1.8 \times 10^{3}}{60.0 \times π}

Solve

x

x \approx 9.5492965855 \approx 9.5493

Conversion Equation

1.0 (\frac{r a d i a n}{m i n u t e \times s e c o n d}) \approx 9.5493 (\frac{c y c l e}{s q u a r e m i n u t e})

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