The rotational version of Newton's law
is
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,
Multiplying both sides by
where we used the definitions
from 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: