# Radius of curvature minimum if velocity is minimum

Q.  The radius of curvature of trajectory for a profile is minimum, if __________
- Published on 21 Sep 15

a. velocity is minimum
b. acceleration is maximum
c. both a. and b.
d. none of the above

#### Discussion

• Sravanthi   -Posted on 15 Dec 15
- The normal component of a particle is perpendicular to the velocity vector and passes through the centre of curvature in curvilinear motion.

- The radius of curvature (ρ) is given as :

(ρ) = v2 / aN

here, v is the velocity of particle and aN is the acceleration in normal direction.

- In the above relation, it is observed that (ρ) is directly proportional to velocity. Hence, when velocity is minimum radius of curvature is minimum.

- (ρ) is inversely proportional to acceleration. Therefore as acceleration increases, radius of curvature (ρ) decreases.

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