The Physics of Amusement Park Rides

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Rides That Spin      Gravitron       carousel                                           
Carousels may not be the most thrill inducing rides at an amusement park but they do help show an interesting phenomenon.

"Centrifugal force" and Newton's First Law of Motion
rotation diagram
When you're riding on a carousel, you feel as if your being push away from the center of the ride. This experience is called centrifugal force, and it's not actually a force. This phenomenon is an example of Newton's first law of motion, which says that an object at rest tends to stays at rest and an object in motion tends to stay in motion. For a carousel to go around in a circle there must be an acceleration pointing toward the center of the ride. The pushing feeling is a result of your body wanting to travel in a straight path while resisting the change in direction caused by the acceleration of the carousel.

Where do you travel fastest on the ride?
On a carousel where is the fastest part of the ride. It depend on the definition of fast. Since a carousel spins we need to look at rotational motion. If we look at the angular velocity which is the change in degrees over change in time, it is the same for every point on the ride since to complete a circle, every point on the rigid body has to travel 360 degrees. However not every point travels the same distance. This makes sense, because a point on the outer edge has to travel a distance equal to the circumference while a point near the center of the ride has to travel a smaller distance in the same amount of time. The relationship between the distance traveled and angular displacement is given by:

distance equation

 where s is the distance traveled, r is the radius and theta is the angle in radians.  If you take the derivative of both sides you get:


Since the radius increases as you move away from the center, this means that the tangential velocity is greatest on the outer edge of the carousel.

Another rid
e that spins is the Gravitron and it is similar to a carousel accept the "centrifugal force" felt by the passengers is significantly stronger. The rapid rotation of this ride allows you to defy gravity as you stick to the wall, let's look at why this happens.

gravitron ridergravitron fbd                                                                                                
If you look at a free body diagram, the magnitude of the normal force and the angle of the slant effects the frictional force in the y-component. As the velocity of the ride increases, the normal force felt on the passengers also increases and this increases the frictional force. If the friction force reaches a high enough magnitude, the vertical component of the friction force will balance out the force of gravity, which will allow that person to not touch the ground of the ride.