Convert dyne to (gram • meter) / square second

Learn how to convert 1 dyne to (gram • meter) / square second step by step.

Calculation Breakdown

Set up the equation

\(1.0\left(dyne\right)={\color{rgb(20,165,174)} x}\left(\dfrac{gram \times meter}{square \text{ } second}\right)\)

Define the base values of the selected units in relation to the SI unit \(\left(newton\right)\)

\(\text{Left side: 1.0 } \left(dyne\right) = {\color{rgb(89,182,91)} 10^{-5}\left(newton\right)} = {\color{rgb(89,182,91)} 10^{-5}\left(N\right)}\)

\(\text{Right side: 1.0 } \left(\dfrac{gram \times meter}{square \text{ } second}\right) = {\color{rgb(125,164,120)} 10^{-3}\left(newton\right)} = {\color{rgb(125,164,120)} 10^{-3}\left(N\right)}\)

Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)

\(1.0\left(dyne\right)={\color{rgb(20,165,174)} x}\left(\dfrac{gram \times meter}{square \text{ } second}\right)\)

\(\text{Insert known values } =>\)

\(1.0 \times {\color{rgb(89,182,91)} 10^{-5}} \times {\color{rgb(89,182,91)} \left(newton\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 10^{-3}}} \times {\color{rgb(125,164,120)} \left(newton\right)}\)

\(\text{Or}\)

\(1.0 \cdot {\color{rgb(89,182,91)} 10^{-5}} \cdot {\color{rgb(89,182,91)} \left(N\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 10^{-3}} \cdot {\color{rgb(125,164,120)} \left(N\right)}\)

\(\text{Cancel SI units}\)

\(1.0 \times {\color{rgb(89,182,91)} 10^{-5}} \cdot {\color{rgb(89,182,91)} \cancel{\left(N\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 10^{-3}} \times {\color{rgb(125,164,120)} \cancel{\left(N\right)}}\)

\(\text{Conversion Equation}\)

\(10^{-5} = {\color{rgb(20,165,174)} x} \times 10^{-3}\)

Cancel factors on both sides

\(\text{Cancel factors}\)

\({\color{rgb(255,204,153)} \cancelto{10^{-2}}{10^{-5}}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{10^{-3}}}\)

\(\text{Simplify}\)

\(10^{-2} = {\color{rgb(20,165,174)} x}\)

Switch sides

\({\color{rgb(20,165,174)} x} = 10^{-2}\)

Solve \({\color{rgb(20,165,174)} x}\)

\({\color{rgb(20,165,174)} x} = 10^{-2}\)

\(\text{Conversion Equation}\)