Why do riders feel pressed to their seats in rotating fair rides?

Riders feel pressed to their seats in rotating fair rides due to the effect of centrifugal force.

In more detail, when a ride starts to rotate, the riders inside are set in motion. According to Newton's first law of motion, an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force. This is also known as the law of inertia. So, when the ride is spinning, the riders want to keep moving in a straight line. However, the seats, which are attached to the ride, exert a force on the riders, causing them to move in a circular path.

This force exerted by the seats is what we call the centripetal force, which is always directed towards the centre of the circle. But for every action, there is an equal and opposite reaction (Newton's third law of motion). So, the riders also exert an equal force on the seats in the opposite direction, away from the centre of the circle. This is the centrifugal force, and it's what makes the riders feel pressed against their seats.

The magnitude of the centrifugal force depends on the mass of the rider, the speed of the ride, and the radius of the circle in which the ride is spinning. The faster the ride or the larger the radius, the greater the centrifugal force, and the stronger the sensation of being pressed against the seat.

It's important to note that the centrifugal force is a 'fictitious' or 'pseudo' force. It doesn't exist in an inertial (non-accelerating) frame of reference. It only appears to exist because we're viewing things from a rotating (accelerating) frame of reference, like the seats of a spinning fair ride. In reality, what's happening is that the riders are trying to move in a straight line (because of inertia), but the seats are constantly pushing them towards the centre of the circle (centripetal force), creating the illusion of a force pushing them outwards (centrifugal force).