Well, as for arbitrary two dimensional curvilinear motion, the acceleration components are:
a_{n}=\frac{v^2}{r}
a_{t}=\frac{dv}{dt}
The first refers to the acceleration components normal to the tangent and thus the second refers to the acceleration components parallel to the tangent.The r...
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I=mv2-mv1
Here I,v1,v2 are all vectors.I is the impulse.v1 is the initial velocity.v2 is the final velocity.Surely you can not say v1-v2=0(remember v1 and v2 are vectors ).
There is a centripetal acceleration for an object that is moving along a non-straight curved path so according to Newton second law there must be a centripetal force,which might be a component of the total force, acting on it .