By: Alize Habib Ahmed Daniyal Mirza Selin Narin ROLLER COASTE RS CIRCULAR MOTION

CIRCULAR MOTION What is a theme park without a roller coaster? You may think that the thrill of riding a roller coaster is derived from the high speeds one experiences, however, the excitement of riding a roller coaster lies in the feelings of weightlessness, weightiness and the acceleration one experiences.

Curved paths such as banked turns and loops are essential in a roller coaster and centripetal acceleration is part of moving in a curved path. Centripetal acceleration and thus circular motion are therefore essential to the successful functioning of roller coasters.

CENTRIPETAL ACCELERATION Centripetal acceleration has two aspects: 1. It is always directed towards the center of the circular path. 2.) It is always in a direction perpendicular to the speed. Velocity v and acceleration a in uniform circular motion at angular rate ω; the speed is constant, but the velocity is always tangent to the orbit; the acceleration has constant magnitude, but always points toward the center of rotation

Acceleration can result from a change in speed and a change in direction:  The change in speed occurs when the roller coaster moves from the bottom of the loop to the top of the loop (it being fastest at the bottom and slowest at the top).  The change in direction occurs as the roller coaster moves right-ward, upward, left-ward and then downward. In this case, there will also be a slight acceleration tangent to the track positively or negatively affecting the speed of the roller coaster. For a roller moving at constant speed, the acceleration will only be centripetal

For the roller coaster to successfully move through a loop, there must be a sufficient centripetal force. This force is always in the direction of the centripetal acceleration, and is the net force that results from adding/subtracting the gravitational force to/from the normal reaction force acting on the roller coaster from the track. CENTRIPETAL FORCE

The gravitational force is always acting downwards (away from the centrer of the circular path) and can be found using F = mg. The normal reaction force must be enough to overcome the gravitational force for there to be a resulting centripetal force that enables the roller coaster to complete the loop.

NEW INSIGHT 1. How does a roller coaster stay in a circular path? Centripetal Force enables the roller coaster to move through the circular path without falling to the ground. 2. How can a roller coaster can hang you upside down and not fall from gravity Right on top of a loop, we feel pressed to our seat, rather than feeling a gravitational attraction towards earth. This feeling, caused by centripetal force acting on us, releases our bodies from the dominant force of gravity(except when we are at the top, because at the top gravity and the centripetal force are acting together) is what makes the rollercoaster experience unique and desired. 3. Why do we love roller coasters? Most cars can obtain the same speed as a roller coaster, therefore, it isn’t the speed that thrills us - it is the acceleration as we move left, right, up and down.

WORKS CITED Harris, Tom. “How Roller Coatsers Work.” science.howstuffworks.com. howstuffworks, n.d. Web. 29 November “Applications of Circular Motion.” thephysicsclassroom.com. Thephysicsclassroom, n.d. Web. 29 November “Roller Coaster G-Forces.” thephysicsclassroom.com. Thephysicsclassroom, n.d. Web. 29 November 2011.