Newton's three laws of motion explain the nature of moving objects. The first, often known as the law of inertia, asserts that an object will continue in its current state of motion (or non-motion) until acted on by an external force. The second law offers the relationship between force, mass, and acceleration. The third law tells us that for every action there is an equal and opposite reaction. These three laws, combined with an understanding of motion perception, can explain the experience of a roller coaster ride in terms of changing direction, forces, and accelerations.
Newton's first law of motion states that an object in motion will tend to remain in motion, and an object at rest will remain at rest, unless an external force acts upon the object. This law is also known as the law of inertia, which explains why objects tend to continue in their current trajectories, even when the system around them undergoes changes. Consider, for example, when you are in a vehicle and it goes around a corner or suddenly brakes or accelerates. You experience the force of the vehicle acting against your body; this is because your body is attempting to move in it's initial trajectory, and the car's trajectory is changing. The seatbelt allows the car to keep you in place by exerting a force on you.
Newton's second law tells us that the acceleration an object undergoes is proportional to its mass and the sum of the forces acting upon it. This law is expressed as the equation F = ma, where F is the sum of all forces, m is the object's mass, and a is the net acceleration. Standard international units of measurement for these quantities are kilograms for mass, meters per second per second for acceleration, and Newtons (in honor of Newton's work on these laws).
Newton's third law states that for every action there is an equal and opposite reaction. What this means is that if you exert a force on an object, that object in turn exerts a force on you, equal in magnitude but opposite in direction. This force is often called the normal force.
There are two primary systems in place that our bodies use to perceive motion. These are both located in the inner ear. The first is known as the semicircular canals. In each ear there is a group of fluid-filled tubes in various orientations. As your head moves, the fluid in these tubes moves, the fluid activates receptors, and the orientation of your head can be determined by your brain. The other system is known as the vestibular system. In the vestibule, tiny pieces of calcium are trapped among a number of tiny hairs known as cilia. These cilia send information to the brain when they are stimulated by the motion of the calcium deposits. Consider the first law of motion; when your body suddenly changes trajectory, the fluid and calcium deposits will be displaced as they try to travel along their current trajectory. This causes a distorting physical sensation of falling or weightlessness, depending on the changes in direction.
When you are riding a roller coaster, you are constantly being subject to rapid changes in motion. These changes in motion are experienced as disturbances in your semicircular canals and vestibules. When the roller coaster car goes around a corner or over a hill, it is accelerating in a different direction. You experience a force as a product of your mass and this acceleration (recall F = ma). The force acting on you causes an acceleration in your body, and your balance and motion systems register changes, which can create a pleasurable thrill.