# A Particle Moves With Constant Speed V Along A Circular Path Of Radius R And Completes The Circle In Time T. The Acceleration Of The Particle Is

As we know:

$$\vec{\Delta}s = \vec{\Delta}Q * \vec{\Delta}r\\\Rightarrow \frac{\vec{\Delta}s}{\Delta t} = \frac{\vec{\Delta}Q}{\Delta t} * \vec{\Delta}r \\\Rightarrow \vec{\Delta}v = \vec{\Delta}w * \vec{\Delta}r = \left | v \right | = wr \\\Rightarrow \vec{a} = \frac{d\vec{v}}{dt} (\vec{w} * \frac{d\vec{v}}{d\vec{t}}) + (\frac{d\vec{w}}{dt} * \vec{r})$$

w = $$\frac{dw}{dt} = 0$$ $$\vec{a} = \vec{w} * \vec{v}$$

OR

a = w v

$$a = \frac{v}{r}, v = \frac{v^{2}}{r}, a = rw^{2}\\\Rightarrow a = rw^{2}\\\Rightarrow r\left [ \frac{2\Pi}{T} \right ]^{2}\\\Rightarrow r * \frac{4\Pi ^{2}}{T^{2}}$$

OR

a = v w

$$v * \frac{2\Pi }{T}$$

Explore more such questions and answers at BYJU’S.