A particle revolving a circular path completes first one third of circumference in 3 sec, while next one third in2 sec. Calculate the average angular velocity of particle
Question
A particle revolving a circular path completes first one third of circumference in 3 sec, while next one third in2 sec. Calculate the average angular velocity of particle
Solution
The average angular velocity (ω_avg) of a particle moving in a circular path is given by the total angle traversed (Δθ) divided by the total time taken (Δt).
In this case, the particle completes 2/3 of the circumference in a total time of 3 sec + 2 sec = 5 sec.
Since a full circle corresponds to an angle of 2π radians, 2/3 of the circumference corresponds to an angle of (2/3) * 2π = 4π/3 radians.
Therefore, the average angular velocity of the particle is:
ω_avg = Δθ / Δt = (4π/3 rad) / 5 sec = 4π/15 rad/sec.
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