Convert revolution / second to radian / hour

Learn how to convert 1 revolution / second to radian / hour step by step.

Calculation Breakdown

Set up the equation

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

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

Right side: 1.0 (\frac{r a d i a n}{h o u r}) = \frac{1.0}{3.6 \times 10^{3}} (\frac{r a d i a n}{s e c o n d}) = \frac{1.0}{3.6 \times 10^{3}} (\frac{r a d}{s})

Insert known values into the conversion equation to determine

x

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

Insert known values =>

1.0 \times 2.0 \times π \times (\frac{r a d i a n}{s e c o n d}) = x \times \frac{1.0}{3.6 \times 10^{3}} \times (\frac{r a d i a n}{s e c o n d})

Or

1.0 \cdot 2.0 \times π \cdot (\frac{r a d}{s}) = x \cdot \frac{1.0}{3.6 \times 10^{3}} \cdot (\frac{r a d}{s})

Cancel SI units

1.0 \times 2.0 \times π \cdot (\frac{r a d}{s}) = x \times \frac{1.0}{3.6 \times 10^{3}} \times (\frac{r a d}{s})

Conversion Equation

2.0 \times π = x \times \frac{1.0}{3.6 \times 10^{3}}

Switch sides

x \times \frac{1.0}{3.6 \times 10^{3}} = π \times 2.0

Isolate

x

Multiply both sides by

(\frac{3.6 \times 10^{3}}{1.0})

x \times \frac{1.0}{3.6 \times 10^{3}} \times \frac{3.6 \times 10^{3}}{1.0} = π \times 2.0 \times \frac{3.6 \times 10^{3}}{1.0}

Cancel

x \times \frac{1.0 \times 3.6 \times 10^{3}}{3.6 \times 10^{3} \times 1.0} = π \times 2.0 \times \frac{3.6 \times 10^{3}}{1.0}

Simplify

x = π \times 2.0 \times 3.6 \times 10^{3}

Solve

x

x \approx 22619.467106 \approx 2.2619 \times 10^{4}

Conversion Equation

1.0 (\frac{r e v o l u t i o n}{s e c o n d}) \approx 2.2619 \times 10^{4} (\frac{r a d i a n}{h o u r})

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