Convert radian / square hour to degree / (hour • second)
Learn how to convert
1
radian / square hour to
degree / (hour • second)
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{radian}{square \text{ } hour}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{degree}{hour \times second}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{radian}{square \text{ } second}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{radian}{square \text{ } hour}\right) = {\color{rgb(89,182,91)} \dfrac{1.0}{1.296 \times 10^{7}}\left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(89,182,91)} \dfrac{1.0}{1.296 \times 10^{7}}\left(\dfrac{rad}{s^{2}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{degree}{hour \times second}\right) = {\color{rgb(125,164,120)} \dfrac{π}{7.2 \times 10^{4}}\left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(125,164,120)} \dfrac{π}{7.2 \times 10^{4}}\left(\dfrac{rad}{s^{2}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{radian}{square \text{ } hour}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{degree}{hour \times second}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1.0}{1.296 \times 10^{7}}} \times {\color{rgb(89,182,91)} \left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{π}{7.2 \times 10^{4}}}} \times {\color{rgb(125,164,120)} \left(\dfrac{radian}{square \text{ } second}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{1.0}{1.296 \times 10^{7}}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{rad}{s^{2}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{π}{7.2 \times 10^{4}}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{rad}{s^{2}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1.0}{1.296 \times 10^{7}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{rad}{s^{2}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{π}{7.2 \times 10^{4}}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{rad}{s^{2}}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{1.0}{1.296 \times 10^{7}} = {\color{rgb(20,165,174)} x} \times \dfrac{π}{7.2 \times 10^{4}}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(\dfrac{1.0}{1.296 \times {\color{rgb(255,204,153)} \cancelto{10^{3}}{10^{7}}}} = {\color{rgb(20,165,174)} x} \times \dfrac{π}{7.2 \times {\color{rgb(255,204,153)} \cancel{10^{4}}}}\)
\(\text{Simplify}\)
\(\dfrac{1.0}{1.296 \times 10^{3}} = {\color{rgb(20,165,174)} x} \times \dfrac{π}{7.2}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{π}{7.2} = \dfrac{1.0}{1.296 \times 10^{3}}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{7.2}{π}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{π}{7.2} \times \dfrac{7.2}{π} = \dfrac{1.0}{1.296 \times 10^{3}} \times \dfrac{7.2}{π}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{π}} \times {\color{rgb(99,194,222)} \cancel{7.2}}}{{\color{rgb(99,194,222)} \cancel{7.2}} \times {\color{rgb(255,204,153)} \cancel{π}}} = \dfrac{1.0 \times 7.2}{1.296 \times 10^{3} \times π}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{7.2}{1.296 \times 10^{3} \times π}\)
Rewrite equation
\(\dfrac{1.0}{10^{3}}\text{ can be rewritten to }10^{-3}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-3} \times 7.2}{1.296 \times π}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0017683883\approx1.7684 \times 10^{-3}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{radian}{square \text{ } hour}\right)\approx{\color{rgb(20,165,174)} 1.7684 \times 10^{-3}}\left(\dfrac{degree}{hour \times second}\right)\)
