Why centripetal force does not increase the value of tangent

[Sbr:132]

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I found in a textbook that the value does not change because the centripetal force is perpendicular to the tangential velocity.

But I am confused, because a vector can have a component, which is perpendicular to the vector.
So if the centripetal force is perpendicular to the tangential velocity, the component of the centripetal force which
is perpendicular to the centripetal force and
_parallel_ to the tangential velocity is reasonable.so according to that centripetal force can increase the value of tangential velocity.I need help.I have searched everywhere but have not got the answer.

 

[rcgldr]

By definition, centripetal force is perpendicular to velocity, so it changes the velocities direction but not the speed. For example, consider a car traveling at constant speed on a winding road, the direction changes, but not the speed.

 

[Sbr:132]

By definition, centripetal force is perpendicular to velocity, so it changes the velocities direction but not the speed. For example, consider a car traveling at constant speed on a winding road, the direction changes, but not the speed.

I know the definition but I want to know why?

 

[A.T.]

a vector can have a component, which is perpendicular to the vector.

You can decompose a vector into multiple vectors, which have non-zero components perpendicular to the original vector. But those components cancel each other out, so they have no net effect.