Convert cycle / (minute • second) to radian / (minute • second)
Learn how to convert
1
cycle / (minute • second) to
radian / (minute • second)
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{cycle}{minute \times second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{radian}{minute \times second}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{radian}{square \text{ } second}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{cycle}{minute \times second}\right) = {\color{rgb(89,182,91)} \dfrac{π}{30.0}\left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(89,182,91)} \dfrac{π}{30.0}\left(\dfrac{rad}{s^{2}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{radian}{minute \times second}\right) = {\color{rgb(125,164,120)} \dfrac{1.0}{60.0}\left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(125,164,120)} \dfrac{1.0}{60.0}\left(\dfrac{rad}{s^{2}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{cycle}{minute \times second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{radian}{minute \times second}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{π}{30.0}} \times {\color{rgb(89,182,91)} \left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{1.0}{60.0}}} \times {\color{rgb(125,164,120)} \left(\dfrac{radian}{square \text{ } second}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{π}{30.0}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{rad}{s^{2}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{1.0}{60.0}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{rad}{s^{2}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{π}{30.0}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{rad}{s^{2}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{1.0}{60.0}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{rad}{s^{2}}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{π}{30.0} = {\color{rgb(20,165,174)} x} \times \dfrac{1.0}{60.0}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{1.0}{60.0} = \dfrac{π}{30.0}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{60.0}{1.0}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{1.0}{60.0} \times \dfrac{60.0}{1.0} = \dfrac{π}{30.0} \times \dfrac{60.0}{1.0}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{1.0}} \times {\color{rgb(99,194,222)} \cancel{60.0}}}{{\color{rgb(99,194,222)} \cancel{60.0}} \times {\color{rgb(255,204,153)} \cancel{1.0}}} = \dfrac{π \times 60.0}{30.0 \times 1.0}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{π \times 60.0}{30.0}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx6.2831853072\approx6.2832\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{cycle}{minute \times second}\right)\approx{\color{rgb(20,165,174)} 6.2832}\left(\dfrac{radian}{minute \times second}\right)\)
