Convert revolution / second to radian / hour
Learn how to convert
1
revolution / second to
radian / hour
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{revolution}{second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{radian}{hour}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{radian}{second}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{revolution}{second}\right) = {\color{rgb(89,182,91)} 2.0 \times π\left(\dfrac{radian}{second}\right)} = {\color{rgb(89,182,91)} 2.0 \times π\left(\dfrac{rad}{s}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{radian}{hour}\right) = {\color{rgb(125,164,120)} \dfrac{1.0}{3.6 \times 10^{3}}\left(\dfrac{radian}{second}\right)} = {\color{rgb(125,164,120)} \dfrac{1.0}{3.6 \times 10^{3}}\left(\dfrac{rad}{s}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{revolution}{second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{radian}{hour}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 2.0 \times π} \times {\color{rgb(89,182,91)} \left(\dfrac{radian}{second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{1.0}{3.6 \times 10^{3}}}} \times {\color{rgb(125,164,120)} \left(\dfrac{radian}{second}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 2.0 \times π} \cdot {\color{rgb(89,182,91)} \left(\dfrac{rad}{s}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{1.0}{3.6 \times 10^{3}}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{rad}{s}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 2.0 \times π} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{rad}{s}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{1.0}{3.6 \times 10^{3}}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{rad}{s}\right)}}\)
\(\text{Conversion Equation}\)
\(2.0 \times π = {\color{rgb(20,165,174)} x} \times \dfrac{1.0}{3.6 \times 10^{3}}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{1.0}{3.6 \times 10^{3}} = π \times 2.0\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{3.6 \times 10^{3}}{1.0}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{1.0}{3.6 \times 10^{3}} \times \dfrac{3.6 \times 10^{3}}{1.0} = π \times 2.0 \times \dfrac{3.6 \times 10^{3}}{1.0}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{1.0}} \times {\color{rgb(99,194,222)} \cancel{3.6}} \times {\color{rgb(166,218,227)} \cancel{10^{3}}}}{{\color{rgb(99,194,222)} \cancel{3.6}} \times {\color{rgb(166,218,227)} \cancel{10^{3}}} \times {\color{rgb(255,204,153)} \cancel{1.0}}} = π \times 2.0 \times \dfrac{3.6 \times 10^{3}}{1.0}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = π \times 2.0 \times 3.6 \times 10^{3}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx22619.467106\approx2.2619 \times 10^{4}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{revolution}{second}\right)\approx{\color{rgb(20,165,174)} 2.2619 \times 10^{4}}\left(\dfrac{radian}{hour}\right)\)
