Convert radian / square minute to revolution / (hour • second)
Learn how to convert
1
radian / square minute to
revolution / (hour • second)
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{radian}{square \text{ } minute}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{revolution}{hour \times second}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{radian}{square \text{ } second}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{radian}{square \text{ } minute}\right) = {\color{rgb(89,182,91)} \dfrac{1.0}{3.6 \times 10^{3}}\left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(89,182,91)} \dfrac{1.0}{3.6 \times 10^{3}}\left(\dfrac{rad}{s^{2}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{revolution}{hour \times second}\right) = {\color{rgb(125,164,120)} \dfrac{π}{1.8 \times 10^{3}}\left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(125,164,120)} \dfrac{π}{1.8 \times 10^{3}}\left(\dfrac{rad}{s^{2}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{radian}{square \text{ } minute}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{revolution}{hour \times second}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1.0}{3.6 \times 10^{3}}} \times {\color{rgb(89,182,91)} \left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{π}{1.8 \times 10^{3}}}} \times {\color{rgb(125,164,120)} \left(\dfrac{radian}{square \text{ } second}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{1.0}{3.6 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{rad}{s^{2}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{π}{1.8 \times 10^{3}}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{rad}{s^{2}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1.0}{3.6 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{rad}{s^{2}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{π}{1.8 \times 10^{3}}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{rad}{s^{2}}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{1.0}{3.6 \times 10^{3}} = {\color{rgb(20,165,174)} x} \times \dfrac{π}{1.8 \times 10^{3}}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(\dfrac{1.0}{3.6 \times {\color{rgb(255,204,153)} \cancel{10^{3}}}} = {\color{rgb(20,165,174)} x} \times \dfrac{π}{1.8 \times {\color{rgb(255,204,153)} \cancel{10^{3}}}}\)
\(\text{Simplify}\)
\(\dfrac{1.0}{3.6} = {\color{rgb(20,165,174)} x} \times \dfrac{π}{1.8}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{π}{1.8} = \dfrac{1.0}{3.6}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.8}{π}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{π}{1.8} \times \dfrac{1.8}{π} = \dfrac{1.0}{3.6} \times \dfrac{1.8}{π}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{π}} \times {\color{rgb(99,194,222)} \cancel{1.8}}}{{\color{rgb(99,194,222)} \cancel{1.8}} \times {\color{rgb(255,204,153)} \cancel{π}}} = \dfrac{1.0 \times 1.8}{3.6 \times π}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1.8}{3.6 \times π}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.1591549431\approx1.5915 \times 10^{-1}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{radian}{square \text{ } minute}\right)\approx{\color{rgb(20,165,174)} 1.5915 \times 10^{-1}}\left(\dfrac{revolution}{hour \times second}\right)\)
