Convert rotation to half circle

Learn how to convert 1 rotation to half circle step by step.

Calculation Breakdown

Set up the equation
\(1.0\left(rotation\right)={\color{rgb(20,165,174)} x}\left(half \text{ } circle\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(radian\right)\)
\(\text{Left side: 1.0 } \left(rotation\right) = {\color{rgb(89,182,91)} 2.0 \times π\left(radian\right)} = {\color{rgb(89,182,91)} 2.0 \times π\left(rad\right)}\)
\(\text{Right side: 1.0 } \left(half \text{ } circle\right) = {\color{rgb(125,164,120)} π\left(radian\right)} = {\color{rgb(125,164,120)} π\left(rad\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(rotation\right)={\color{rgb(20,165,174)} x}\left(half \text{ } circle\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 2.0 \times π} \times {\color{rgb(89,182,91)} \left(radian\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} π}} \times {\color{rgb(125,164,120)} \left(radian\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 2.0 \times π} \cdot {\color{rgb(89,182,91)} \left(rad\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} π} \cdot {\color{rgb(125,164,120)} \left(rad\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 2.0 \times π} \cdot {\color{rgb(89,182,91)} \cancel{\left(rad\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} π} \times {\color{rgb(125,164,120)} \cancel{\left(rad\right)}}\)
\(\text{Conversion Equation}\)
\(2.0 \times π = {\color{rgb(20,165,174)} x} \times π\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\({\color{rgb(255,204,153)} \cancel{π}} \times 2.0 = {\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{π}}\)
\(\text{Simplify}\)
\(2.0 = {\color{rgb(20,165,174)} x}\)
Switch sides
\({\color{rgb(20,165,174)} x} = 2.0\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x} = 2\)
\(\text{Conversion Equation}\)
\(1.0\left(rotation\right) = {\color{rgb(20,165,174)} 2}\left(half \text{ } circle\right)\)

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