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Circular Motion: Radial & Tangential Acceleration

Watch how a particle's acceleration splits into a radial part that bends the path and, when the speed itself changes, a tangential part that stretches or shrinks the velocity vector.

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t (s)0.00
θ (deg)0.0
ω (rad/s)0.00
T = 2π/ω (s)0.00
α (rad/s²)0.00
v |v|0.00
v̂ₓ0.000
v̂ᵧ0.000
a_r = v²/r0.00
a_r,x0.000
a_r,y0.000
a_t = dv/dt0.00
a_t,x0.000
a_t,y0.000
a = √(a_r²+a_t²)0.00
velocity, v radial accel, a_r = v²/r tangential accel, a_t = dv/dt net accel, a

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Parameters

Formulas

Radial (always present) a_r = v²r = 0.00
Tangential (zero only if uniform) v = v₀·eᵏᵗ + e⁻ᵏᵗ2  →  a_t = dvdt = 0.00
Total acceleration a = √a_r² + a_t² = 0.00

In uniform circular motion only a_r acts, so a = a_r and the particle keeps constant speed. In non-uniform circular motion a_t also acts, so the total acceleration a is always ≥ a_r — the speed is visibly stretching or shrinking as the particle goes around.

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