Convert radian / square hour to cycle / square second
Learn how to convert
1
radian / square hour to
cycle / square second
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{radian}{square \text{ } hour}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{cycle}{square \text{ } second}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{radian}{square \text{ } second}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{radian}{square \text{ } hour}\right) = {\color{rgb(89,182,91)} \dfrac{1.0}{1.296 \times 10^{7}}\left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(89,182,91)} \dfrac{1.0}{1.296 \times 10^{7}}\left(\dfrac{rad}{s^{2}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{cycle}{square \text{ } second}\right) = {\color{rgb(125,164,120)} 2.0 \times π\left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(125,164,120)} 2.0 \times π\left(\dfrac{rad}{s^{2}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{radian}{square \text{ } hour}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{cycle}{square \text{ } second}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1.0}{1.296 \times 10^{7}}} \times {\color{rgb(89,182,91)} \left(\dfrac{radian}{square \text{ } second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 2.0 \times π}} \times {\color{rgb(125,164,120)} \left(\dfrac{radian}{square \text{ } second}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{1.0}{1.296 \times 10^{7}}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{rad}{s^{2}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 2.0 \times π} \cdot {\color{rgb(125,164,120)} \left(\dfrac{rad}{s^{2}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1.0}{1.296 \times 10^{7}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{rad}{s^{2}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 2.0 \times π} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{rad}{s^{2}}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{1.0}{1.296 \times 10^{7}} = {\color{rgb(20,165,174)} x} \times 2.0 \times π\)
Switch sides
\({\color{rgb(20,165,174)} x} \times π \times 2.0 = \dfrac{1.0}{1.296 \times 10^{7}}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{π \times 2.0}\right)\)
\({\color{rgb(20,165,174)} x} \times π \times 2.0 \times \dfrac{1.0}{π \times 2.0} = \dfrac{1.0}{1.296 \times 10^{7}} \times \dfrac{1.0}{π \times 2.0}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{π}} \times {\color{rgb(99,194,222)} \cancel{2.0}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{π}} \times {\color{rgb(99,194,222)} \cancel{2.0}}} = \dfrac{1.0 \times 1.0}{1.296 \times 10^{7} \times π \times 2.0}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1.0}{1.296 \times 10^{7} \times π \times 2.0}\)
Rewrite equation
\(\dfrac{1.0}{10^{7}}\text{ can be rewritten to }10^{-7}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-7}}{1.296 \times π \times 2.0}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0000000123\approx1.228 \times 10^{-8}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{radian}{square \text{ } hour}\right)\approx{\color{rgb(20,165,174)} 1.228 \times 10^{-8}}\left(\dfrac{cycle}{square \text{ } second}\right)\)