Tangential and normal acceleration

On a curved path, the acceleration can be resolved into two perpendicular components: a normal (radial) component directed towards the center of curvature of the curve and a tangential component tangential to the path.
Tangential acceleration:
at = 0 only if the speed is constant (uniform motion), so at exists only when the speed varies. The tangential acceleration occurs due to the change in the speed of the moving object.
Characteristics of tangential acceleration at a point M:
Origin: M
Line of action: tangent to the trajectory of the moving object
Direction:
- along the direction of motion (same as velocity) in accelerated
motion
- opposite to the direction of motion in decelerated motion
(Figure 12-b)
Magnitude: ‖at ‖ = |(d V)/dt| = |V' | , where V is the speed
Radial (normal) acceleration:
an is always in the direction of un since it is directed towards the center of curvature of the curve. In rectilinear motion, R → ∞, so an = 0. Therefore, an exists only in curvilinear motion, where the direction of the velocity of the object is continuously varying.
The normal acceleration occurs due to the change in the direction of the velocity of the moving object.
Characteristics of the normal acceleration at a point M:
Origin: M
Line of action: along the principal normal to the trajectory at M
Direction: towards the center of curvature of the trajectory at M (centripetal)
Magnitude: an = V^2/R , where V is the speed and R is the radius of curvature of the trajectory at M
at is tangent to the trajectory and an is directed toward the center of curvature of the path; therefore, in curvilinear motion the acceleration vector is directed towards the ‘interior’ of the path.
You can watch:
1) Position vector in a plane :    • Position vector in a plane  
2) Displacement vector in a plane :    • Displacement vector in a plane  
3) Equation of trajectory in a plane :    • Equation of trajectory in a plane  
4) Average and instantaneous velocity vectors :    • Average and instantaneous velocity ve...  
5) Average and instantaneous acceleration :    • Average and instantaneous acceleratio...