Question

A particle is moving along a circle of radius 10 metre at a constant speed of 5 metre per second find (i)centripetal acceleration and (ii)angular speed of the particle.

Answer 1

$\large\sf\underline{Understand\: Concept}$

As per given in the information,a particle which is moving along a circle whose radius is 10 metre and speed is given 5 m/s so now first of all,we will find acceleration and after that angular velocity and we know formula of acceleration is velocity square by radius and formula of angular velocity is velocity by radius.So now let's solve!

$\large\sf\underline{Given:-}$

•Velocity of a particle moving along a circle is 5m/s.

•Radius of that circle is 10m.

$\large\sf\underline{To\:Find:-}$

•Centripetal acceleration of that particle.

•Angular Speed of that particle.

$\large\sf\underline{Formula\:used}$

$\: \: \sf \: formula \: of \: centripetal \: acceleration = \frac{ {v}^{2} }{r}$

$\: \: \sf \: formula \: of \: angular \: velocity \: of \: the \: particle( \omega)= \frac{v}{r}$

$\large\sf\underline{Solution:-}$

Given:-

• v = 5m/s
• r = 10m

$\: \: \sf \: a = \frac{ {v}^{2} }{r}$

Now substitute the values

$\: \: \sf \: a = \frac{ {5}^{2} }{10} = \frac{25}{10} = 2.5 \frac{m}{ {s}^{2} }$

Hence, centripetal acceleration of particle is 2.5 m/s^2.

Now we will find angular velocity

$\: \: \sf \: angular \: velocity( \omega) = \frac{v}{r}$

Now substitute the values,

$\: \: \sf \: angular \: velocity = \frac{5}{10} = 0.5 \frac{radian}{ {s}^{2} }$

Hence, angular velocity of a particle is 0.5 radian/s^2.

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