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.
