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The study aims at discussing the physics behind design and action of roller coasters by first stating the definition of a roller coaster. A roller coaster is a type of amusement ride that employs a form of elevated railroad track design with tight turns, steep slopes and sometimes inversions (Wikipedia). The roller coaster applies a wide knowledge of physics concepts of work and energy mainly potential energy and kinetic energy, gravity and some uniform circular motion too in cases where the roller coasters take circular paths. Gravity plays a huge part in roller coaster physics. As the coaster gets higher, the cars are pulled down faster by gravity and move faster along the tracks. Friction forces also play a role in roller coasters and Newton’s first law of motion. The study briefly gives the origin of roller coasters and principles used then and now.

History of Roller Coasters

Roller coasters originated from the Russian ice slides. The slides first appeared during the 17th century throughout Russia; with concentration in the area that would become St. Petersburg. The structures were built out of lumber with a sheet of ice several inches thick covering the surface. Riders climbed the stairs attached to back of the slide, sped down the 50-degree drop and ascend the stirs of the stairs that lay parallel (and opposite) to the first one. It is known that by 1817 two coasters were built in France, known as the Russian Mountains of Belleville and the Aerial Walk. Several upgrades have been made and now there are several types of steel roller coasters. The Aerial Walk featured a heart-shaped layout with two tracks that flowed in opposite directions from the central tower. They then went around the course, came together at the bottom and ascend parallel lift hills. The first looping coaster was located in Frascati Gardens in Paris, France. The hill was 43 feet high, had a 13-foot-wide loop, and was tested with everything under the sun before humans were allowed on. The layout was simple: the rider rode down the gentle slope on a small cart and through a meal small circle.

The Physics Behind Design and Action of Roller Coasters

One’s body feels accelerated in a funny way when a coaster car is speeding up and pulled into the seat. This applies Newton’s first law of motion, which states that a body remains in its state of rest or motion in a straight line unless acted upon by an external force – the law of inertia. Similarly, if the coaster accelerates down fast enough, the upward acceleration force exceeds the downward force of gravity, making you feel like you are being pulled upward if you are accelerating up a steep hill; the acceleration force and gravity are pulling in roughly the same direction, making you feel heavier than normal. That explains the laws of physics related to the roller coaster and one’s body. As you go around a loop-the-loop, your inertia not only produces an exciting acceleration force, but also keeps you in the seat when upside down. This applies uniform circular motion.

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The underlying principle of all roller coasters is the law of conservation of energy, which states that energy can neither be created nor destroyed, but transformed from one form to another. In roller coasters, the two forms of energy that are most important are gravitational potential energy and kinetic energy. Gravitational potential energy is the energy that than an object has due to its height and is equal to the objects mass multiplied by the height multiplied by the gravitational constant (PE=mgh). Gravitational potential energy is greatest at the highest point of a roller coaster and least at the lowest point. Kinetic energy on the other hand is the energy an object has due to its motion and is equal to a half multiplied by the mass of the object multiplied by its velocity squared (KE= 1/2mv2). The kinetic energy is greatest at the bottom and lowest at the top. This implies that the roller coaster is fastest at the bottom. Potential energy and kinetic energy can be exchanged for one another, so at certain points the car of the roller coaster may just have potential energy (at top), just kinetic energy (bottom), and combination of both at all the other points. The first hill of the rollercoaster is always the highest part of the roller coaster because friction and drag immediately begin robbing the car of energy. At the top of the first hill the cars energy is almost entirely gravitational potential energy (because its velocity is zero or almost zero). This is the maximum energy that the car will have during the ride.

Friction exists in all roller coasters, and it takes away from the useful energy provided by the roller coaster. Friction is caused in roller coasters by the rubbing of the car wheels on the track and by rubbing of air (and sometimes water) against the cars. Friction turns the useful energy of the roller-coaster to heat energy, which is unnecessary. Friction is also the reason that roller coasters can never regain their maximum height after the initial hill, unless a second chain lift is incorporated somewhere on the track, and they can’t go forever.

Cars can only make it through loops if they have enough speed at the top of the loop. Tis minimum speed is referred to as critical velocity, and is equal to the square root of the radius of the loop multiplied by the gravitational constant (vc= (rg)1/2). Most roller coaster loops are not perfectly circular in shape, but have a teardrop shape called clothoid. Roller coaster designers discovered that if a loop is circular, the rider experiences the greatest force at the bottom of the loop when the cars are moving fastest, following the principle of maximum tension in a vertical circle at the bottom of uniform circular motion. After many riders sustained neck injuries, looping roller coasters were abandoned in 1901 and revived in 1976 when Revolution at Six Flags Magic Mountain became the first looping roller coaster using a clothoid shape. In a clothoid shape, the radius of curvature of the loop is widest at the bottom, reducing the force on the riders when the cars move fastest and smallest at the top when the cars are moving relatively slowly.


In conclusion, roller coasters in amusement parks are upgraded and designed basically taking in to account physics laws practically in their motion, design shapes and safety. They borrow physics concepts of gravity, uniform circular motion in the loop types, Newton’s first law of motion – the inertia law, friction and the backbone concept being the law of conservation of energy. Numerous forces are involved in the daily motion of roller coasters too to ensure perfect functioning of the roller coaster and to keep it in balance.


  1. Sandy. A., 2007. The Beginning of Roller-Coasters. Article (online) Available at: Accessed 25/01/19.
  2. Harris. T., 2010. How Roller Coasters Work. Article (online) Available at:

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