The Acceleration associated with uniform circular motion is called a centripetal acceleration.
Let a particle of mass (m), moving with a constant speed (v), angular velocity (ω), on a circular path of radius r with centre O. Let at any time t, the particle be at P, and at time t+∆t the particle be at point Q.
∠POQ = ∆θ and |r₁| = |r₂| = r
Let v₁ and v₂ be the velocity vectors of the particle at location P and Q respectively.
Since, the particle is moving with a uniform speed (v) the length of the tangents at P and Q are equal i.e |v₁| = |v₂| = v
Note:- The angle between two lines is the same to the angle between their perpendicular lines.
Since, bottom angles are equal and included sides are proportional, then these two Triangles will be similar.
Now, By using properties of similarity.