Convert radian / hour to hertz

Learn how to convert 1 radian / hour to hertz step by step.

Calculation Breakdown

Set up the equation

\(1.0\left(\dfrac{radian}{hour}\right)={\color{rgb(20,165,174)} x}\left(hertz\right)\)

Define the base values of the selected units in relation to the SI unit \(\left(hertz\right)\)

\(\text{Left side: 1.0 } \left(\dfrac{radian}{hour}\right) = {\color{rgb(89,182,91)} \dfrac{0.159155}{3.6 \times 10^{3}}\left(hertz\right)} = {\color{rgb(89,182,91)} \dfrac{0.159155}{3.6 \times 10^{3}}\left(Hz\right)}\)

\(\text{Right side: 1.0 } \left(hertz\right) = {\color{rgb(125,164,120)} 1.0\left(hertz\right)} = {\color{rgb(125,164,120)} 1.0\left(Hz\right)}\)

Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)

\(1.0\left(\dfrac{radian}{hour}\right)={\color{rgb(20,165,174)} x}\left(hertz\right)\)

\(\text{Insert known values } =>\)

\(1.0 \times {\color{rgb(89,182,91)} \dfrac{0.159155}{3.6 \times 10^{3}}} \times {\color{rgb(89,182,91)} \left(hertz\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 1.0}} \times {\color{rgb(125,164,120)} \left(hertz\right)}\)

\(\text{Or}\)

\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{0.159155}{3.6 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \left(Hz\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 1.0} \cdot {\color{rgb(125,164,120)} \left(Hz\right)}\)

\(\text{Cancel SI units}\)

\(1.0 \times {\color{rgb(89,182,91)} \dfrac{0.159155}{3.6 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(Hz\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 1.0} \times {\color{rgb(125,164,120)} \cancel{\left(Hz\right)}}\)

\(\text{Conversion Equation}\)

\(\dfrac{0.159155}{3.6 \times 10^{3}} = {\color{rgb(20,165,174)} x} \times 1.0\)

\(\text{Simplify}\)

\(\dfrac{0.159155}{3.6 \times 10^{3}} = {\color{rgb(20,165,174)} x}\)

Switch sides

\({\color{rgb(20,165,174)} x} = \dfrac{0.159155}{3.6 \times 10^{3}}\)

Rewrite equation

\(\dfrac{1.0}{10^{3}}\text{ can be rewritten to }10^{-3}\)

\(\text{Rewrite}\)

\({\color{rgb(20,165,174)} x} = \dfrac{10^{-3} \times 0.159155}{3.6}\)

Solve \({\color{rgb(20,165,174)} x}\)

\({\color{rgb(20,165,174)} x}\approx0.0000442097\approx4.421 \times 10^{-5}\)