The formula of angular velocity cannot be fully understood! In the formula of angular velocity (i.e. w = 2P / T), isn't 2p a fixed value (i.e. 360 °)? Why can it be calculated by the angle equal to the actual rotation angle (e.g. 90 °)? If it is known that the angular velocity of a circular motion of an object is 50m / s, it only rotates 90 °, can it be directly removed by 2p, and the actual rotation time t (T) can be obtained by the angular velocity of 50M / S?

The formula of angular velocity cannot be fully understood! In the formula of angular velocity (i.e. w = 2P / T), isn't 2p a fixed value (i.e. 360 °)? Why can it be calculated by the angle equal to the actual rotation angle (e.g. 90 °)? If it is known that the angular velocity of a circular motion of an object is 50m / s, it only rotates 90 °, can it be directly removed by 2p, and the actual rotation time t (T) can be obtained by the angular velocity of 50M / S?

The unit of ω is: radians per second, that is, the rotation angle in unit time. = 2 π / T, t is the rotation angle in one cycle, and the rotation angle in one cycle is just 2 π. T is not the actual time t
50M / S is the linear velocity V, which is 50m per second
To convert it into angular velocity, you need to convert how many radians it is to walk 50 meters per second
V / 2 π r = R / S (R / s)
(R / s) * 2 π = ω (rad / s)
That's about it. I hope it's useful for you