A particle completes 4 revolution per second on a circular path of radius 0.25m. calculate the angular velvet city and the centripital acceleration of the particles
To calculate the angular velocity and the centripetal acceleration of a particle, we need to use the formula:
Angular Velocity (ω) = (2π * n) / t
where n is the number of revolutions and t is the time taken. In this case, the particle completes 4 revolutions per second, so n = 4 and t = 1 second.
Let's calculate the angular velocity:
ω = (2π * 4) / 1
= 8π radians/second
So, the angular velocity of the particle is 8π radians/second.
Now, let's calculate the centripetal acceleration. The formula for centripetal acceleration is:
Centripetal Acceleration (a) = (ω^2) * r
where ω is the angular velocity and r is the radius of the circular path. In this case, the radius is given as 0.25 meters.
Let's calculate the centripetal acceleration:
a = (8π)^2 * 0.25
= 64π^2 * 0.25
= 16π^2 meters/second^2
So, the centripetal acceleration of the particle is 16π^2 meters/second^2.