Convert degree / (hour • second) to degree / square hour
Learn how to convert
1
degree / (hour • second) to
degree / square hour
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{degree}{hour \times second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{degree}{square \text{ } hour}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{radian}{square \text{ } second}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{degree}{hour \times second}\right) = {\color{rgb(89,182,91)} \dfrac{π}{7.2 \times 10^{4}}\left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(89,182,91)} \dfrac{π}{7.2 \times 10^{4}}\left(\dfrac{rad}{s^{2}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{degree}{square \text{ } hour}\right) = {\color{rgb(125,164,120)} \dfrac{π}{2.3328 \times 10^{9}}\left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(125,164,120)} \dfrac{π}{2.3328 \times 10^{9}}\left(\dfrac{rad}{s^{2}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{degree}{hour \times second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{degree}{square \text{ } hour}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{π}{7.2 \times 10^{4}}} \times {\color{rgb(89,182,91)} \left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{π}{2.3328 \times 10^{9}}}} \times {\color{rgb(125,164,120)} \left(\dfrac{radian}{square \text{ } second}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{π}{7.2 \times 10^{4}}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{rad}{s^{2}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{π}{2.3328 \times 10^{9}}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{rad}{s^{2}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{π}{7.2 \times 10^{4}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{rad}{s^{2}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{π}{2.3328 \times 10^{9}}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{rad}{s^{2}}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{π}{7.2 \times 10^{4}} = {\color{rgb(20,165,174)} x} \times \dfrac{π}{2.3328 \times 10^{9}}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(\dfrac{{\color{rgb(255,204,153)} \cancel{π}}}{7.2 \times {\color{rgb(99,194,222)} \cancel{10^{4}}}} = {\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{π}}}{2.3328 \times {\color{rgb(99,194,222)} \cancelto{10^{5}}{10^{9}}}}\)
\(\text{Simplify}\)
\(\dfrac{1.0}{7.2} = {\color{rgb(20,165,174)} x} \times \dfrac{1.0}{2.3328 \times 10^{5}}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{1.0}{2.3328 \times 10^{5}} = \dfrac{1.0}{7.2}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{2.3328 \times 10^{5}}{1.0}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{1.0}{2.3328 \times 10^{5}} \times \dfrac{2.3328 \times 10^{5}}{1.0} = \dfrac{1.0}{7.2} \times \dfrac{2.3328 \times 10^{5}}{1.0}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{1.0}} \times {\color{rgb(99,194,222)} \cancel{2.3328}} \times {\color{rgb(166,218,227)} \cancel{10^{5}}}}{{\color{rgb(99,194,222)} \cancel{2.3328}} \times {\color{rgb(166,218,227)} \cancel{10^{5}}} \times {\color{rgb(255,204,153)} \cancel{1.0}}} = \dfrac{{\color{rgb(255,204,153)} \cancel{1.0}} \times 2.3328 \times 10^{5}}{7.2 \times {\color{rgb(255,204,153)} \cancel{1.0}}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{2.3328 \times 10^{5}}{7.2}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x} = 32400 = 3.24 \times 10^{4}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{degree}{hour \times second}\right) = {\color{rgb(20,165,174)} 3.24 \times 10^{4}}\left(\dfrac{degree}{square \text{ } hour}\right)\)
