The document discusses the concept of curvature and normal vectors of a plane curve as a particle moves along it. It explains that the tangent vector, which is a unit vector, changes direction but not length during the motion along the curve. The curvature quantifies the rate of turning of the tangent vector per unit length of the curve.

1. Muhammad Ahmad
(L1F20BSPH0040)
Curvature and
Normal
Vectors of a
Curve

2. Curvature of a Plane Curve
As a particle moves along a smooth curve in the plane, T =
𝑑𝒓
𝑑𝑠
turns as the
curve bends. Since T is a unit vector, its length remains constant and only its
direction changes as the particle moves along the curve. The rate at which T
turns per unit of length along the curve is called the curvature.

6. Examples: