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

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

Answer 2

Time, T = 2.62 seconds

Step-by-step 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{(a)/(r)}`

`\omega=\sqrt{(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=(2\pi)/(\omega)`

`T=(2\pi)/(2.39)`

T = 2.62 seconds

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