* *

* *

*Centripetal
Acceleration*

Curves are an essential part
of a roller coaster, and centripetal acceleration is part of moving in a
circular path. Therefore, centripetal
acceleration is also an essential part of a roller coaster.

Centripetal
acceleration points toward the center of the circular path of the train, but is
felt by passengers as a force pushing them to the outer edge of the circular
path. This feeling is often described
as centrifugal force, although there is no actual force pushing or pulling
passengers away from the circle. The
“centrifugal force” is actually your body’s inertia, or its resistance to the
train’s change in direction: your body wants to continue in a straight line and
attempts to do so as the train turns.
Luckily, your body is strapped into the roller coaster train, otherwise
your body would continue in the straight path that the train was following
before it entered the curve.

The equation for
centripetal acceleration is:

a* _{r}* = v

Where a* _{r}*
is centripetal acceleration, v is velocity in meters per second, and r is the
radius of the circle in meters. This
means that the higher the train’s velocity, the greater the centripetal
acceleration. This also means that the
smaller the curve of the path being traveled, the greater the centripetal
acceleration. Because of this, many
high-speed roller coasters use banked turns rather than the flat ones that are
safe for slower speeds. Banking the
turns in a roller coaster gives you the feeling of being pushed into your seat
rather than being thrown to the side of the car.

**Back to Roller Coaster
Physics**