Drag the sliders to see a = v² ÷ r come alive: the gold arrow is the tangential velocity, the wine arrow is the centripetal acceleration that always points to the centre. Then cut the string and watch the mass fly off along the tangent.
velocity (tangent)acceleration (to centre)
Centripetal acceleration a = v² ÷ r
25.00 m/s²
= 2.55 g
Centripetal force F = m·v² ÷ r25.00 N
Angular velocity ω = v ÷ r5.00 rad/s
Period T = 2πr ÷ v1.257 s
Frequency f = 1 ÷ T0.796 Hz
Radius r1.00 m
Speed v5.0 m/s
Mass m1.0 kg
The wine arrow (centripetal acceleration) always points to the centre; the gold arrow (velocity) stays tangent to the circle.
Try it: change the mass — only the force F responds. The acceleration a, angular velocity ω, period T and frequency f never depend on mass.