Convert radian / square hour to revolution / square second

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

Calculation Breakdown

Set up the equation
$$1.0\left(\dfrac{radian}{square \text{ } hour}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{revolution}{square \text{ } second}\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(\dfrac{radian}{square \text{ } second}\right)$$
$$\text{Left side: 1.0 } \left(\dfrac{radian}{square \text{ } hour}\right) = {\color{rgb(89,182,91)} \dfrac{1.0}{1.296 \times 10^{7}}\left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(89,182,91)} \dfrac{1.0}{1.296 \times 10^{7}}\left(\dfrac{rad}{s^{2}}\right)}$$
$$\text{Right side: 1.0 } \left(\dfrac{revolution}{square \text{ } second}\right) = {\color{rgb(125,164,120)} 2.0 \times π\left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(125,164,120)} 2.0 \times π\left(\dfrac{rad}{s^{2}}\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(\dfrac{radian}{square \text{ } hour}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{revolution}{square \text{ } second}\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} \dfrac{1.0}{1.296 \times 10^{7}}} \times {\color{rgb(89,182,91)} \left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 2.0 \times π}} \times {\color{rgb(125,164,120)} \left(\dfrac{radian}{square \text{ } second}\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} \dfrac{1.0}{1.296 \times 10^{7}}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{rad}{s^{2}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 2.0 \times π} \cdot {\color{rgb(125,164,120)} \left(\dfrac{rad}{s^{2}}\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} \dfrac{1.0}{1.296 \times 10^{7}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{rad}{s^{2}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 2.0 \times π} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{rad}{s^{2}}\right)}}$$
$$\text{Conversion Equation}$$
$$\dfrac{1.0}{1.296 \times 10^{7}} = {\color{rgb(20,165,174)} x} \times 2.0 \times π$$
Switch sides
$${\color{rgb(20,165,174)} x} \times π \times 2.0 = \dfrac{1.0}{1.296 \times 10^{7}}$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{1.0}{π \times 2.0}\right)$$
$${\color{rgb(20,165,174)} x} \times π \times 2.0 \times \dfrac{1.0}{π \times 2.0} = \dfrac{1.0}{1.296 \times 10^{7}} \times \dfrac{1.0}{π \times 2.0}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{π}} \times {\color{rgb(99,194,222)} \cancel{2.0}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{π}} \times {\color{rgb(99,194,222)} \cancel{2.0}}} = \dfrac{1.0 \times 1.0}{1.296 \times 10^{7} \times π \times 2.0}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{1.0}{1.296 \times 10^{7} \times π \times 2.0}$$
Rewrite equation
$$\dfrac{1.0}{10^{7}}\text{ can be rewritten to }10^{-7}$$
$$\text{Rewrite}$$
$${\color{rgb(20,165,174)} x} = \dfrac{10^{-7}}{1.296 \times π \times 2.0}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x}\approx0.0000000123\approx1.228 \times 10^{-8}$$
$$\text{Conversion Equation}$$
$$1.0\left(\dfrac{radian}{square \text{ } hour}\right)\approx{\color{rgb(20,165,174)} 1.228 \times 10^{-8}}\left(\dfrac{revolution}{square \text{ } second}\right)$$