Introduction:
When a particle moves in a circle, it experiences centripetal acceleration towards the center of the circle. This acceleration can be caused by a force acting towards the center, such as gravity or tension in a string. The magnitude of this acceleration is given by the equation a = ω^2 * r, where ω is the angular velocity and r is the radius of the circle. The angular acceleration, α, is the rate at which the angular velocity changes with time.

Given:
- Radius of the circle, r
- Initial velocity, Vo
- Number of rounds completed, n

Calculating angular velocity:
The particle starts from rest, so its initial angular velocity, ωo, is 0. To find its final angular velocity, ω, we need to calculate the distance traveled in terms of the circumference of the circle. The distance traveled is equal to 2πrn, where n is the number of rounds completed. Therefore, the final angular velocity can be calculated using the equation:
ω = (2πrn) / t,
where t is the time taken to complete n rounds.

Calculating angular acceleration:
The angular acceleration, α, is the rate at which the angular velocity changes with time. It can be calculated using the equation:
α = (ω - ωo) / t,
where ω is the final angular velocity and ωo is the initial angular velocity.

Explanation:
1. Calculate the final angular velocity, ω, using the equation ω = (2πrn) / t, where r is the radius and n is the number of rounds completed.
2. Calculate the angular acceleration, α, using the equation α = (ω - ωo) / t, where ωo is the initial angular velocity (0 in this case) and t is the time taken to complete n rounds.
3. Substitute the values of ω and ωo into the equation to calculate α.
4. The resulting value will be the angular acceleration of the particle.

Conclusion:
The angular acceleration of the particle can be calculated by finding the final angular velocity using the equation ω = (2πrn) / t and then applying the formula α = (ω - ωo) / t. The value obtained will represent the rate at which the angular velocity changes with time.