Question

please prove centripetal accleration by not using similar triangles

Answer 1

We can find a simple expressio for the magnitude of the acceleration in uniform circular motion.We begin with the below diagram,which shows a particle moving with constant speed in a circular path of radius RRwith center at OO . The particle moves a distance ΔsΔs from P1P1 to P2P2 in a time interval ΔtΔt. The figure below also shows the vector change in velocity Δv⃗ Δv→ during this interval. The angles labeled ΔϕΔϕ in the figure are the same because v1→v1→ is perpendicular to the line OP1OP1and v2→v2→ is perpendicular to the line OP2OP2. Hence the triangle in the figure are similar.