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Circular motion summary

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.