a particle takes 6.28seconds to complete one revolution.its angular speed is
3.14 rad/s
To find the angular speed of a particle, we need to know the angle through which the particle moves and the time taken to complete that motion. In this case, if the particle takes 6.28 seconds to complete one revolution, we can use this information to find the angular speed.
The angle through which the particle moves in one revolution is 360 degrees or 2π radians. Therefore, the time taken to complete one revolution is the same as the angle through which the particle moves.
Angular speed (ω) is defined as the angle (θ) covered per unit time (t). Mathematically, it can be expressed as:
ω = θ / t
Since the particle completes one revolution (θ = 2π) in 6.28 seconds (t = 6.28), we can substitute these values into the formula to find the angular speed:
ω = 2π / 6.28
Evaluating the expression, we get:
ω ≈ 0.318 radians per second
Therefore, the angular speed of the particle is approximately 0.318 radians per second.