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# Newton’s 1st & 2nd law in rotation

• Forces cause acceleration dampened by inertia (mass)’. That is Newton’s 2nd law:1 $$\sum \vec F=m\vec a\tag{2nd law}$$
• Does ‘angular forces (torques) similarly cause angular acceleration dampened by angular inertia’? Yes, indeed! There is an equivalent of Newton’s 2nd law for rotation (see Proof 24): $$\sum \vec \tau=I\vec \alpha\tag{2nd law}$$

And an ‘angular force’ is what we called ‘torque’ $\tau$, while ‘angular inertia’ dampening the torque’s effect of course is the moment-of-inertia $I$.

Of course, Newton’s 1st law, which is achieved by setting $\vec a=0$ in the 2nd law, is likewise achieved by setting $\vec \alpha=0$ in the rotational version of the 2nd law:

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