Convert radian / square second to degree / (minute • second)
Learn how to convert
1
radian / square second to
degree / (minute • second)
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{radian}{square \text{ } second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{degree}{minute \times second}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{radian}{square \text{ } second}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{radian}{square \text{ } second}\right) = {\color{rgb(89,182,91)} 1.0\left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(89,182,91)} 1.0\left(\dfrac{rad}{s^{2}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{degree}{minute \times second}\right) = {\color{rgb(125,164,120)} \dfrac{π}{1.08 \times 10^{4}}\left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(125,164,120)} \dfrac{π}{1.08 \times 10^{4}}\left(\dfrac{rad}{s^{2}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{radian}{square \text{ } second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{degree}{minute \times second}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 1.0} \times {\color{rgb(89,182,91)} \left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{π}{1.08 \times 10^{4}}}} \times {\color{rgb(125,164,120)} \left(\dfrac{radian}{square \text{ } second}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 1.0} \cdot {\color{rgb(89,182,91)} \left(\dfrac{rad}{s^{2}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{π}{1.08 \times 10^{4}}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{rad}{s^{2}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 1.0} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{rad}{s^{2}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{π}{1.08 \times 10^{4}}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{rad}{s^{2}}\right)}}\)
\(\text{Conversion Equation}\)
\(1.0 = {\color{rgb(20,165,174)} x} \times \dfrac{π}{1.08 \times 10^{4}}\)
\(\text{Simplify}\)
\(1.0 = {\color{rgb(20,165,174)} x} \times \dfrac{π}{1.08 \times 10^{4}}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{π}{1.08 \times 10^{4}} = 1.0\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.08 \times 10^{4}}{π}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{π}{1.08 \times 10^{4}} \times \dfrac{1.08 \times 10^{4}}{π} = 1.0 \times \dfrac{1.08 \times 10^{4}}{π}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{π}} \times {\color{rgb(99,194,222)} \cancel{1.08}} \times {\color{rgb(166,218,227)} \cancel{10^{4}}}}{{\color{rgb(99,194,222)} \cancel{1.08}} \times {\color{rgb(166,218,227)} \cancel{10^{4}}} \times {\color{rgb(255,204,153)} \cancel{π}}} = 1.0 \times \dfrac{1.08 \times 10^{4}}{π}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1.08 \times 10^{4}}{π}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx3437.7467708\approx3.4377 \times 10^{3}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{radian}{square \text{ } second}\right)\approx{\color{rgb(20,165,174)} 3.4377 \times 10^{3}}\left(\dfrac{degree}{minute \times second}\right)\)
