v=ds/dt=rdθ/dt=rω

a=dv/dt=rdω/dr=rα

This is a derivative problem of higher mathematics. First of all, we should understand the basic concepts of linear velocity, angular velocity, acceleration and linear acceleration. A is linear acceleration and α is angular acceleration. Because it is equivalent to α=dω/dt and v=ωr, a=dv/dt=dωr/dt=rdω/dt=rα, which is often used in the study of curvilinear motion and rigid body rotation.

Extended data:

Let a particle make a circular motion around particle O on the oxygen plane. If at time t, the particle is at point A, and the radius OA forms an angle θ with the Ox axis, it is called angular position. At time t+Δ t, the particle reaches point B, and the radius OB forms an angle θ +Δθ with the Ox axis. That is to say, in Δ t time, the particle rotates through the angle Δ θ, which is called the angular displacement of the particle to the O point. Angular displacement has not only magnitude, but also steering. Generally speaking, the angular displacement in the counterclockwise direction is positive and the angular displacement in the clockwise direction is negative.

Baidu encyclopedia-angular velocity