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 gives
where we used the definitions and . Furthermore, the left-hand side is the definition of torque . Thus, we have derived
from Newton's second law applied to the tangential force and acceleration of the mass .
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: