Convert cycle / hour to radian / second

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

Calculation Breakdown

Set up the equation
\(1.0\left(\dfrac{cycle}{hour}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{radian}{second}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{radian}{second}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{cycle}{hour}\right) = {\color{rgb(89,182,91)} \dfrac{π}{1.8 \times 10^{3}}\left(\dfrac{radian}{second}\right)} = {\color{rgb(89,182,91)} \dfrac{π}{1.8 \times 10^{3}}\left(\dfrac{rad}{s}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{radian}{second}\right) = {\color{rgb(125,164,120)} 1.0\left(\dfrac{radian}{second}\right)} = {\color{rgb(125,164,120)} 1.0\left(\dfrac{rad}{s}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{cycle}{hour}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{radian}{second}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{π}{1.8 \times 10^{3}}} \times {\color{rgb(89,182,91)} \left(\dfrac{radian}{second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 1.0}} \times {\color{rgb(125,164,120)} \left(\dfrac{radian}{second}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{π}{1.8 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{rad}{s}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 1.0} \cdot {\color{rgb(125,164,120)} \left(\dfrac{rad}{s}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{π}{1.8 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{rad}{s}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 1.0} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{rad}{s}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{π}{1.8 \times 10^{3}} = {\color{rgb(20,165,174)} x} \times 1.0\)
\(\text{Simplify}\)
\(\dfrac{π}{1.8 \times 10^{3}} = {\color{rgb(20,165,174)} x}\)
Switch sides
\({\color{rgb(20,165,174)} x} = \dfrac{π}{1.8 \times 10^{3}}\)
Rewrite equation
\(\dfrac{1.0}{10^{3}}\text{ can be rewritten to }10^{-3}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-3} \times π}{1.8}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0017453293\approx1.7453 \times 10^{-3}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{cycle}{hour}\right)\approx{\color{rgb(20,165,174)} 1.7453 \times 10^{-3}}\left(\dfrac{radian}{second}\right)\)

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