Rotational Kinematics and the Linear–Angular Connection

The same four equations, in angular clothing

Angular position $\theta$ (in radians), angular velocity $\omega=\Delta\theta/\Delta t$ and angular acceleration $\alpha=\Delta\omega/\Delta t$ obey exactly the constant-acceleration equations of Unit 1 with $x\to\theta$, $v\to\omega$, $a\to\alpha$:

Graph rules carry over too: the slope of a $\theta$–$t$ graph is $\omega$, the slope of an $\omega$–$t$ graph is $\alpha$, and the area under an $\omega$–$t$ graph is the angle turned through. The one new habit is unit discipline: convert revolutions to radians ($1$ rev $=2\pi$ rad) and rpm to rad/s ($\omega=\frac{2\pi N}{60}$) before substituting.

Linking a point on the rim to the rotation

Every point on a rigid rotating body shares the same $\omega$ and $\alpha$, but points farther from the axis move faster and farther:

The tangential acceleration $a_t$ changes the speed; the centripetal acceleration $a_c$ changes the direction and exists even when $\alpha=0$. A wheel of radius $0{,}3$ m spun from rest at $\alpha=2$ rad/s² has, after $5$ s, $\omega=10$ rad/s; a point on its rim moves at $v=3$ m/s with $a_t=0{,}6$ m/s² and $a_c=30$ m/s² — the centripetal part dominates almost immediately. The total acceleration of the point is the vector sum, $\sqrt{a_t^2+a_c^2}$, since the two are perpendicular.

Which direction is positive?

Pick counter-clockwise as positive unless told otherwise, and keep it. A wheel slowing while spinning clockwise has $\omega \lt 0$ and $\alpha \gt 0$ — the same "opposite signs mean slowing down" rule as in linear motion.