Short-duration forces
In circular motion , it is said that the centripetal force acts only for a very very short period of time , hence is able to only change the direction but not magnitude of the velocity .
Similarly in a collision , the impulsive-collision forces act for a very short period of time , but they are able to change the direction as well as magnitude of velocity , considering an inelastic collision . The collision lasts for a very short period of time , almost instantaneous (with reference to newtonian mechanics , not considering einstein's special relativity).
*Why is that ? Why is collision force able to change magnitude when it acts for a short period of time as well ?
The reasoning that collision forces have a very high magnitude won't work here,as say they have a magnitude $100,000 N$ , then imagine the circular motion to be of a mass $1kg$ and speed$100,000 ms^{-1}$ and radius $1m$ , now we have both centripetal and collision forces equal but still centripetal force is able to only change direction .
Similarly we can always adjust both the forces and circle's radii accordingly , so that impulse provided by both the forces , centripetal and collision forces are always equal .
we calculate impulse provided by the centripetal force in circular motion to be such that
for the differential time $dt$ ,
we evaluate impulse for ,the force remains constant in terms of both
magnitude and direction and according to continuity of time ,
there are infinite of such instances giving us a non-zero length span of such a time .
The reasoning that centripetal force acts perpendicular to direction of motion also won't work since then problem will be asking that momentum doesn't change even in the direction of the force which is perpendicular to path, even in the perpendicular direction there is no impulse and if there's impulse , it may lead to violation of Energy conservation , which can't happen .
These two mode of reasoning , I have tried and they fail here .
All conditions are sort of idealistic here, following all of <PERSON>'s and <PERSON>'s laws.
All masses are to be considered to be point masses .
Impulse is $\int^{t_2} _{t_1} Fdt$ where '$F$' is the force and '$t_2-t_1$' is the span of time of finite length we considered .
Also please provide an intuitive answer as well . 512