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, [tex]a=4.7\ m/s^2[/tex]
To find,
Time taken to complete one revolution.
Solution,
The centripetal acceleration of the particle in circular path is given by :
[tex]a=\omega^2 r[/tex]
[tex]\omega[/tex] is the angular velocity of the particle
[tex]\omega=\sqrt{\dfrac{a}{r}}[/tex]
[tex]\omega=\sqrt{\dfrac{4.7}{0.82}}[/tex]
[tex]\omega=2.39\ rad/s[/tex]
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 :
[tex]T=\dfrac{2\pi}{\omega}[/tex]
[tex]T=\dfrac{2\pi}{2.39}[/tex]
T = 2.62 seconds
So, the time taken to complete one revolution is 2.62 seconds.
