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LESSON NOTES

Definition of Centripetal Force

Merry-go-rounds are a perfect example of how a force is used to keep an object moving
in a circular path. Your body wanted to fly off the merry-go-round in a straight line, but
your hands exerted an opposing force to keep you on. The tendency for your body to fly
off the merry-go-round is called centrifugal force. It isn't a real force, but an apparent
one. The force you used with your hands to stay on the ride is real, and it is
called centripetal force.
Centripetal force is a force on an object directed to the center of a circular path that
keeps the object on the path. Its value is based on three factors: 1) the velocity of the
object as it follows the circular path; 2) the object's distance from the center of the path;
and 3) the mass of the object.
Centrifugal force, on the other hand, is not a force, but a tendency for an object to
leave the circular path and fly off in a straight line. Sometimes people mistakenly say
'centrifugal force' when they mean 'centripetal force.' The velocity of the object is
constant and perpendicular to a line running from the object to the center of the circle; it
is called tangential velocity.

An object on a circular path

In this diagram, centripetal force f is shown as a red arrow. It is constant in magnitude
but keeps changing direction so that it is always pointing to the center. Also shown on
the diagram is the tangential velocity, v. Finally, the constant distance of the object from
the center of the circle is represented by the variable r, or radius.

How is the Centripetal Force Calculated?

The Centripetal Force Formula is given as the product of mass (in kg) and tangential
velocity (in meters per second) squared, divided by the radius (in meters) which implies
that on doubling the tangential velocity, the centripetal force will be quadrupled.
Mathematically it is written as: