Question

A particle travels in a circle of radius 82 cm and with a centripetal acceleration of 4.7 m/s2. How long does the particle take to complete one revolution?

Answer 1

Answer:

Time, T = 2.62 seconds

Explanation:

Given that,

Radius of the circular path, r = 82 cm = 0.82 m

Centripetal acceleration of the particle, $a=4.7\ m/s^2$

To find,

Time taken to complete one revolution.

Solution,

The centripetal acceleration of the particle in circular path is given by :

$a=\omega^2 r$

$\omega$ is the angular velocity of the particle

$\omega=\sqrt{\dfrac{a}{r}}$

$\omega=\sqrt{\dfrac{4.7}{0.82}}$    

$\omega=2.39\ rad/s$

Let T is the time taken by the particle take to complete one revolution. The relation between the angular velocity and the time is given by :

$T=\dfrac{2\pi}{\omega}$

$T=\dfrac{2\pi}{2.39}$

T = 2.62 seconds

So, the time taken to complete one revolution is 2.62 seconds.

Answer 2

Acceleration = r w²              radius r = 0.82 meter    angular velocity w

4.7  =  0.82  w²   
So  w = 2.394  radians / sec
Time period T = time duration for completing one revolution =  2 π / w
           = 2π / 2.394  = 2.624 seconds