Question

Does the central force normal to the motion ? Why , why not ?

Answer 1

No, The direction of central force is not normal to the motion. Answer lies in the basic properties of central force, I'll try to give you intuitive idea with help of some basic equation.

Central force: In classical mechanics, a central force on an object is a force that is directed along the line joining the object and the origin. i.e It is always directed radially towards the object.

(Only relevant) Property of Central force:

1. The path of the particle must be a plane curve, i.e., it must lie in a plane.

2. The angular momentum of the particle is conserved, i.e., it is constant in time.

L= r x p (L, r and p are standard notation of angular momentum, distance and Momentum respectively)

For a motion where no other force then central force is applied on the particle,

L remains constant which equals to:

Hence, No conclusion can be made for angle to be 90 degrees always.

If the angle between r and v is not 90 deg, then the angle between central force (As central force is in r direction only) and v can't be 90 deg always.

Example: Motion under gravitational force with eccentricity of orbit not equal to 0 (Circle) are the example where velocity isn't perpendicular to the central force.

For better understanding try to derive the equation of orbit in equivalent one dimensional problem, You will get orbits like, ellipse, hyperbola and parabola and also circle( where central force is perpendicular to the motion)