Convert cycle / second to radian / second
Learn how to convert
1
cycle / second to
radian / second
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{cycle}{second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{radian}{second}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(hertz\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{cycle}{second}\right) = {\color{rgb(89,182,91)} 1.0\left(hertz\right)} = {\color{rgb(89,182,91)} 1.0\left(Hz\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{radian}{second}\right) = {\color{rgb(125,164,120)} 0.159155\left(hertz\right)} = {\color{rgb(125,164,120)} 0.159155\left(Hz\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{cycle}{second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{radian}{second}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 1.0} \times {\color{rgb(89,182,91)} \left(hertz\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 0.159155}} \times {\color{rgb(125,164,120)} \left(hertz\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 1.0} \cdot {\color{rgb(89,182,91)} \left(Hz\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 0.159155} \cdot {\color{rgb(125,164,120)} \left(Hz\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 1.0} \cdot {\color{rgb(89,182,91)} \cancel{\left(Hz\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 0.159155} \times {\color{rgb(125,164,120)} \cancel{\left(Hz\right)}}\)
\(\text{Conversion Equation}\)
\(1.0 = {\color{rgb(20,165,174)} x} \times 0.159155\)
\(\text{Simplify}\)
\(1.0 = {\color{rgb(20,165,174)} x} \times 0.159155\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 0.159155 = 1.0\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{0.159155}\right)\)
\({\color{rgb(20,165,174)} x} \times 0.159155 \times \dfrac{1.0}{0.159155} = 1.0 \times \dfrac{1.0}{0.159155}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{0.159155}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{0.159155}}} = 1.0 \times \dfrac{1.0}{0.159155}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1.0}{0.159155}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx6.2831830605\approx6.2832\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{cycle}{second}\right)\approx{\color{rgb(20,165,174)} 6.2832}\left(\dfrac{radian}{second}\right)\)
