Convert radian / hour to degree / hour
Learn how to convert
1
radian / hour to
degree / hour
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{radian}{hour}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{degree}{hour}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{radian}{second}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{radian}{hour}\right) = {\color{rgb(89,182,91)} \dfrac{1.0}{3.6 \times 10^{3}}\left(\dfrac{radian}{second}\right)} = {\color{rgb(89,182,91)} \dfrac{1.0}{3.6 \times 10^{3}}\left(\dfrac{rad}{s}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{degree}{hour}\right) = {\color{rgb(125,164,120)} \dfrac{π}{6.48 \times 10^{5}}\left(\dfrac{radian}{second}\right)} = {\color{rgb(125,164,120)} \dfrac{π}{6.48 \times 10^{5}}\left(\dfrac{rad}{s}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{radian}{hour}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{degree}{hour}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1.0}{3.6 \times 10^{3}}} \times {\color{rgb(89,182,91)} \left(\dfrac{radian}{second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{π}{6.48 \times 10^{5}}}} \times {\color{rgb(125,164,120)} \left(\dfrac{radian}{second}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{1.0}{3.6 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{rad}{s}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{π}{6.48 \times 10^{5}}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{rad}{s}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1.0}{3.6 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{rad}{s}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{π}{6.48 \times 10^{5}}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{rad}{s}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{1.0}{3.6 \times 10^{3}} = {\color{rgb(20,165,174)} x} \times \dfrac{π}{6.48 \times 10^{5}}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(\dfrac{1.0}{3.6 \times {\color{rgb(255,204,153)} \cancel{10^{3}}}} = {\color{rgb(20,165,174)} x} \times \dfrac{π}{6.48 \times {\color{rgb(255,204,153)} \cancelto{10^{2}}{10^{5}}}}\)
\(\text{Simplify}\)
\(\dfrac{1.0}{3.6} = {\color{rgb(20,165,174)} x} \times \dfrac{π}{6.48 \times 10^{2}}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{π}{6.48 \times 10^{2}} = \dfrac{1.0}{3.6}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{6.48 \times 10^{2}}{π}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{π}{6.48 \times 10^{2}} \times \dfrac{6.48 \times 10^{2}}{π} = \dfrac{1.0}{3.6} \times \dfrac{6.48 \times 10^{2}}{π}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{π}} \times {\color{rgb(99,194,222)} \cancel{6.48}} \times {\color{rgb(166,218,227)} \cancel{10^{2}}}}{{\color{rgb(99,194,222)} \cancel{6.48}} \times {\color{rgb(166,218,227)} \cancel{10^{2}}} \times {\color{rgb(255,204,153)} \cancel{π}}} = \dfrac{1.0 \times 6.48 \times 10^{2}}{3.6 \times π}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{6.48 \times 10^{2}}{3.6 \times π}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx57.295779513\approx57.2958\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{radian}{hour}\right)\approx{\color{rgb(20,165,174)} 57.2958}\left(\dfrac{degree}{hour}\right)\)