Exploring Motion in a Vertical Circle: A Simple Ride Model

This is simple simulation for exploring simple circular motion type rides.Part of what makes these rides thrilling is the apparent sideways "force".  The effect is due to inertia (an object in motion tends to stay in motion in a straight line). This effect is commonly referred to as the centrifugal force. The circular motion experience is used in a wide variety of amusement park rides and is even used by NASA and the Air Force to train pilots and astronauts as well as study the effects of high accelerations. The size of the effect depends upon the speed of the circular motion as well as the radius of the circle. 

The rotational speed ω and radial distance R are controlled with buttons at the bottom of the applet.  These buttons  increase or decrease the settings for ω and R.  Changing the set ride control does not instantaneously, the ride instead smoothly transitions to the new setting. The effect is that the controls are "lagged" to eliminate the unphysical results of "slamming" the simulation controls and creating unreasonable accelerations.

The net horizontal force on the riders is monitored in the accompanying graph in terms of "g's", that is, in terms of multiples of the rider's weight. The simulation will also display force vectors and a graph of the g-forces versus time. The units for are radians per second while the units for R are meters, the usual choice for these units in physics.

Challenges:

• How does the rotational speed ω affect the force felt by the riders?
• How does the radius R affect the force felt by the riders
• What is the greatest force you can get out of this ride? Consider the ramifications in terms of the physiological impact of g-forces.

Examples: