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

Learn how to convert 1 radian / (minute • second) to cycle / square hour 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 h o u r})

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 h o u r}) = \frac{π}{6.48 \times 10^{6}} (\frac{r a d i a n}{s q u a r e s e c o n d}) = \frac{π}{6.48 \times 10^{6}} (\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 h o u r})

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}{6.48 \times 10^{6}} \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}{6.48 \times 10^{6}} \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}{6.48 \times 10^{6}} \times (\frac{r a d}{s^{2}})

Conversion Equation

\frac{1.0}{60.0} = x \times \frac{π}{6.48 \times 10^{6}}

Switch sides

x \times \frac{π}{6.48 \times 10^{6}} = \frac{1.0}{60.0}

Isolate

x

Multiply both sides by

(\frac{6.48 \times 10^{6}}{π})

x \times \frac{π}{6.48 \times 10^{6}} \times \frac{6.48 \times 10^{6}}{π} = \frac{1.0}{60.0} \times \frac{6.48 \times 10^{6}}{π}

Cancel

x \times \frac{π \times 6.48 \times 10^{6}}{6.48 \times 10^{6} \times π} = \frac{1.0 \times 6.48 \times 10^{6}}{60.0 \times π}

Simplify

x = \frac{6.48 \times 10^{6}}{60.0 \times π}

Solve

x

x \approx 34377.467708 \approx 3.4377 \times 10^{4}

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 3.4377 \times 10^{4} (\frac{c y c l e}{s q u a r e h o u r})

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