Newton's Second Law for Rotations
The rotational version of Newton's law is
where









![\begin{eqnarray*}
\tau &=& \dot{L} \,\eqss \, I\dot{\omega}\,\isdefss \, I\alpha\\ [5pt]
f &=& \dot{p} \,\eqss \, m\dot{v}\,\isdefss \, ma
\end{eqnarray*}](http://www.dsprelated.com/josimages_new/pasp/img2949.png)
To show that Eq.(B.28) results from Newton's second law
,
consider again a mass
rotating at a distance
from an axis
of rotation, as in §B.4.3 above, and
let
denote a tangential force on the mass, and
the corresponding tangential acceleration. Then we have, by Newton's
second law,











In summary, force equals the time-derivative of linear momentum, and torque equals the time-derivative of angular momentum. By Newton's laws, the time-derivative of linear momentum is mass times acceleration, and the time-derivative of angular momentum is the mass moment of inertia times angular acceleration:

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Equations of Motion for Rigid Bodies
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Torque