Kinematics of a particle moving on a curve
Now
.............................(1)
What does this expression show? The acceleration is composed of two parts. One part is tangential to curve and is equal to the rate of change of speed. The other part is in the direction of 
, which is the rate of change of unit tangent vector with respect to distance. If the particle is moving in a straight line, 
remains constant. Hence the second part will vanish. But if the curve is not straight, the second part will be present. Let us try to understand this part. For that we review some concepts from the differential geometry.
, which is the rate of change of unit tangent vector with respect to distance. If the particle is moving in a straight line, remains constant. Hence the second part will vanish. But if the curve is not straight, the second part will be present. Let us try to understand this part. For that we review some concepts from the differential geometry.