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# Summary of circular motion

Uniform circular motion : $v=\text{constant}$ (the direction of velocity changes).

• Acceleration is perpendicular to the trajectory

Non-uniform circular motion : $v\neq\text{constant}$.

• acceleration has a non-zero component in the direction of motion

Angular displacement : $\vecphy{\theta}=\vecphy{s}/r$

Angular velocity: $\vecphy{\omega}=\vecphy{\theta}/t$

Tangential linear velocity $\vecphy{v}=r\vecphy{\omega}$

Period is the time taken for one revolution.

Frequency is the number of revolutions per unit of time $f=1/T$

$$\omega=\frac{2\pi}{T}=2\pi f$$

Centripetal force (perpendicular to the direction of motion):$$F_c=\frac{mv^{2}}{r}$$

Centripetal acceleration (directed towards the centre of circular motion): $$a_c=\frac{v^{2}}{r}$$

$m=$mass; $r=$radius of circular motion.