Key Equations

Key Equations

6.1 Angle of Rotation and Angular Velocity

Angle of rotation	$\text{Δ}\theta =\frac{\text{Δ}s}{r}$
Angular speed:	$\omega =\frac{\text{Δ}\theta }{\text{Δ}t}$
Tangential speed:	$v=r\omega$

6.2 Uniform Circular Motion

Centripetal acceleration	$a_{\text{c}}=\frac{v^2}{r}$ or $a_c=r{\omega }^2$
Centripetal force	$F_c=m{a}_c$, $F_{\text{c}}=m\frac{v^2}{r}$, $F_{\text{c}}=mr{\omega }^2$

6.3 Rotational Motion

Constant angular velocity
Angular acceleration	$\text{α}=\frac{\text{Δ}\text{ω}}{\text{Δ}t}$
Constant angular acceleration
Rotational kinematic equations	$\theta =\text{ω}t$, $\text{ω}={\text{ω}}_0+\text{α}t$, $\theta ={\text{ω}}_{0}t+\frac{1}{2}\text{α}{t}^2$, ${\text{ω}}^2={\text{ω}}_0{}^2+2\text{α}\theta$
Tangential (linear) acceleration	$a=r\text{α}$
Torque	$\tau =rF\sin \theta$