# Convert revolution / square second to cycle / (hour • second)

Learn how to convert 1 revolution / square second to cycle / (hour • second) step by step.

## Calculation Breakdown

Set up the equation
$$1.0\left(\dfrac{revolution}{square \text{ } second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{cycle}{hour \times second}\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(\dfrac{radian}{square \text{ } second}\right)$$
$$\text{Left side: 1.0 } \left(\dfrac{revolution}{square \text{ } second}\right) = {\color{rgb(89,182,91)} 2.0 \times π\left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(89,182,91)} 2.0 \times π\left(\dfrac{rad}{s^{2}}\right)}$$
$$\text{Right side: 1.0 } \left(\dfrac{cycle}{hour \times second}\right) = {\color{rgb(125,164,120)} \dfrac{π}{1.8 \times 10^{3}}\left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(125,164,120)} \dfrac{π}{1.8 \times 10^{3}}\left(\dfrac{rad}{s^{2}}\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(\dfrac{revolution}{square \text{ } second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{cycle}{hour \times second}\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} 2.0 \times π} \times {\color{rgb(89,182,91)} \left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{π}{1.8 \times 10^{3}}}} \times {\color{rgb(125,164,120)} \left(\dfrac{radian}{square \text{ } second}\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} 2.0 \times π} \cdot {\color{rgb(89,182,91)} \left(\dfrac{rad}{s^{2}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{π}{1.8 \times 10^{3}}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{rad}{s^{2}}\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} 2.0 \times π} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{rad}{s^{2}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{π}{1.8 \times 10^{3}}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{rad}{s^{2}}\right)}}$$
$$\text{Conversion Equation}$$
$$2.0 \times π = {\color{rgb(20,165,174)} x} \times \dfrac{π}{1.8 \times 10^{3}}$$
Cancel factors on both sides
$$\text{Cancel factors}$$
$${\color{rgb(255,204,153)} \cancel{π}} \times 2.0 = {\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{π}}}{1.8 \times 10^{3}}$$
$$\text{Simplify}$$
$$2.0 = {\color{rgb(20,165,174)} x} \times \dfrac{1.0}{1.8 \times 10^{3}}$$
Switch sides
$${\color{rgb(20,165,174)} x} \times \dfrac{1.0}{1.8 \times 10^{3}} = 2.0$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{1.8 \times 10^{3}}{1.0}\right)$$
$${\color{rgb(20,165,174)} x} \times \dfrac{1.0}{1.8 \times 10^{3}} \times \dfrac{1.8 \times 10^{3}}{1.0} = 2.0 \times \dfrac{1.8 \times 10^{3}}{1.0}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{1.0}} \times {\color{rgb(99,194,222)} \cancel{1.8}} \times {\color{rgb(166,218,227)} \cancel{10^{3}}}}{{\color{rgb(99,194,222)} \cancel{1.8}} \times {\color{rgb(166,218,227)} \cancel{10^{3}}} \times {\color{rgb(255,204,153)} \cancel{1.0}}} = 2.0 \times \dfrac{1.8 \times 10^{3}}{1.0}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = 2.0 \times 1.8 \times 10^{3}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x} = 3600 = 3.6 \times 10^{3}$$
$$\text{Conversion Equation}$$
$$1.0\left(\dfrac{revolution}{square \text{ } second}\right) = {\color{rgb(20,165,174)} 3.6 \times 10^{3}}\left(\dfrac{cycle}{hour \times second}\right)$$

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