It is often believed that, when turning in a car, you lean the opposite way of the turn. Turn right, you feel a force left. This is a common misconception.
In actuality, as the car turns right, our bodies' inertia (directly proportional to mass) keeps us wanting to travel in a straight line, which is why we feel thrust leftward. This is also why, when we slam on the breaks, our bodies jerk forward - they want to keep going straight.
The above explanation makes sense, but I've always wondered why we didn't feel a force inward in circular motion if the centripetal force points to the center of the circle. So I did some research, and learned some more about it.
An inward net force is required to make a turn in a circle: the centripetal force. In the absence of any net force, an object in motion continues in motion in a straight line at constant speed (Newton's first law: an object in motion stays in motion unless acted upon by an outside force).
In a right-turning car, the passenger slides left. In a sense, the car is beginning to slide out from under the passenger. Once they strike the left door of the car (or their seatbelt holds them in place), the passenger can now turn with the car and experience some circular motion. There is never any outward force exerted upon them. The passenger is either moving straight ahead in the absence of a force or moving along a circular path in the presence of an inward-directed force - the centripetal force.
The car itself is what provides the inward centripetal force, even if we as the passengers don't feel the force directly.
So hopefully that clears up any questions you had about feeling centripetal force. I'd been confused about this concept for over a year now, so researching it definitely helped me understand it better!
Until next time,