Question

Derive an expression for velocity and acceleration for uniform circular motion

Answer 1

If an object moves in a circle it changes its velocity i.e. it is accelerating.

we know that centripetal force is given as

F = mv2/r

now, as

F = ma

thus,

ma = mv2/r

so, linear acceleration will be

a = v2/r = w2r

Answer 2

Explanation:

When an object moving in circular path, it will said to move under uniform circular motion. We know that velocity is equal total displacement per unit time. It is given by :

$v=\dfrac{d}{t}$

Angular velocity is,

$\omega=\dfrac{\Delta \theta}{\Delta t}$

Since, $\theta=\dfrac{l}{r}$

$\Delta\theta=\dfrac{\Delta l}{r}$

The angular velocity in terms of angular displacement is given by :

$v=r\omega$

r is radius of circular path

The rate of change of angular velocity is called angular acceleration. It is given by :

$a=\dfrac{v^2}{r}$

or

$a=r\omega^2$

Hence, this is the required solution.

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