Convert radian / minute to degree / minute
Learn how to convert
1
radian / minute to
degree / minute
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{radian}{minute}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{degree}{minute}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{radian}{second}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{radian}{minute}\right) = {\color{rgb(89,182,91)} \dfrac{1.0}{60.0}\left(\dfrac{radian}{second}\right)} = {\color{rgb(89,182,91)} \dfrac{1.0}{60.0}\left(\dfrac{rad}{s}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{degree}{minute}\right) = {\color{rgb(125,164,120)} \dfrac{π}{1.08 \times 10^{4}}\left(\dfrac{radian}{second}\right)} = {\color{rgb(125,164,120)} \dfrac{π}{1.08 \times 10^{4}}\left(\dfrac{rad}{s}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{radian}{minute}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{degree}{minute}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1.0}{60.0}} \times {\color{rgb(89,182,91)} \left(\dfrac{radian}{second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{π}{1.08 \times 10^{4}}}} \times {\color{rgb(125,164,120)} \left(\dfrac{radian}{second}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{1.0}{60.0}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{rad}{s}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{π}{1.08 \times 10^{4}}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{rad}{s}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1.0}{60.0}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{rad}{s}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{π}{1.08 \times 10^{4}}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{rad}{s}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{1.0}{60.0} = {\color{rgb(20,165,174)} x} \times \dfrac{π}{1.08 \times 10^{4}}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{π}{1.08 \times 10^{4}} = \dfrac{1.0}{60.0}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.08 \times 10^{4}}{π}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{π}{1.08 \times 10^{4}} \times \dfrac{1.08 \times 10^{4}}{π} = \dfrac{1.0}{60.0} \times \dfrac{1.08 \times 10^{4}}{π}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{π}} \times {\color{rgb(99,194,222)} \cancel{1.08}} \times {\color{rgb(166,218,227)} \cancel{10^{4}}}}{{\color{rgb(99,194,222)} \cancel{1.08}} \times {\color{rgb(166,218,227)} \cancel{10^{4}}} \times {\color{rgb(255,204,153)} \cancel{π}}} = \dfrac{1.0 \times 1.08 \times 10^{4}}{60.0 \times π}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1.08 \times 10^{4}}{60.0 \times π}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx57.295779513\approx57.2958\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{radian}{minute}\right)\approx{\color{rgb(20,165,174)} 57.2958}\left(\dfrac{degree}{minute}\right)\)