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So what is the centrifugal force. Think of the fairground ride called
the rotor. You get in, it starts spinning and the floor falls away, but
you stay held against the wall. In the earth frame, the only horizontal
force acting on you is the horizontal component of the normal force by
the wall (the wall may not be completely vertical.) This is true for the
same reasons I described above.
In your accelerating frame you feel an outward force pushing you against
the wall. That is the centrifugal force. It only exists in the
accelerating frame. A similar situation existed in an accelerating car.
When the car is accelerating forward, what force pushes you back in the
seat? You feel pushed back but that is your sensation of the forward force
by the seat on you. If the driver slams on the brakes, what force pushes
you into the windshield, or hopefully into the seat belt...there is none,
you continue to move forward (N1) until the windshield or the seat belt
slows you motion.