At an instant, the velocity and acceleration of a particle make an angle θ. If its speed is v and acceleration magnitude is a, the radius of curvature is:
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At an instant, the velocity and acceleration of a particle make an angle θ. If its speed is v and acceleration magnitude is a, the radius of curvature is:

G1 Physics · Accepted Answer

The acceleration component normal to the velocity is aₙ = a sinθ. Since aₙ = v²/R, we get R = v²/(a sinθ).