Question

Derive an expression for the centripetal acceleration of a body moving with uniform speed V along a circular path of radius R . Give its direction also ​

Answer 1

Explanation:-

Q. To derive an expression for centripetal acceleration of circular motion.

Derivation:-

we know that the position vector of time t is :-

→$\vec{r} = \vec{OP} = OP \vec{e_r}$

• where $e_r$ is the radial unit vector.

→$r ( \hat{i}Cos\theta + \hat{j}Sin\theta )$

• Differentiating with respect to the time.

→$\vec{v} = \dfrac{d\vec{r}}{dt}$

→$\vec{v}= \dfrac{d[r(\hat{i}Cos\theta + \hat{j}Sin\theta )]}{dt}$

→$\vec{v} = r\left[ \hat{i}\left(-Sin\theta \dfrac{d\theta}{dt}\right)+\hat{j}\left(Cos\theta \dfrac{d\theta}{dt}\right)\right]$

→$\vec{v}= r\omega [-\hat{i}Sin\theta + \hat{j}Cos\theta ]$

• Where $\omega$ is angular velocity.

Next is in attachment.

Answer 2

Answer:

In the attachment

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