a particle completes 4 revolution/sec on a circular path of radius 0.25m.calculate angular velocity

n=4

w = 2πn/t
= 2π4/1
= 8π rad/sec

Angular velocity is defined as the rate of change of angular displacement. To calculate the angular velocity, we need to determine the angular displacement covered by the particle in a given time period.

Given that the particle completes 4 revolutions per second, we need to convert this information to angular displacement.

To convert revolutions to radians, we can use the relationship:

1 revolution = 2π radians

Now, we can calculate the angular displacement:

Angular displacement (in radians) = Number of revolutions * 2π

Angular displacement = 4 * 2π

Angular displacement = 8π radians

Since angular velocity is the rate of change of angular displacement per unit time, we divide the angular displacement by the time taken:

Angular velocity = Angular displacement / Time

In this case, the time period is 1 second, as the particle completes 4 revolutions per second.

Angular velocity = 8π radians / 1 second

Therefore, the angular velocity is 8π radians/second, or approximately 25.12 radians/second.

Well done

n=4 rev/s

angular velocity ω =2πn =8π rad/s
linear velocity v= ωR