Question

Obtain the radial and angular components of acceleration for a particle moving under the influence of central force

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Answer 1

Given that,

A particle moving under the influence of central force.

Center force :

Central force defined as the force that is acting on an object which is directed along the line joining the object and the origin.

Centripetal force is central force when an object is moving in a circular path with uniform speed.

The constant force acts towards the center of the circle.

We know that,

A particle moving under the influence of central force then the radial acceleration.

We need to calculate the radial acceleration

Using centripetal force

$F = \dfrac{mv^2}{r}$

$ma=\dfrac{mv^2}{r}$

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

This is the radial component of acceleration.

Angular acceleration :

Angular acceleration is equal to the change in angular velocity divided by change in time.

In mathematically term,

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

Hence, The radial component of acceleration is $\dfrac{v^2}{r}$

The angular component of acceleration is $\dfrac{\Delta\omega}{\Delta t}$