Centripetal force
Figure 1: A simple example corresponding to
uniform circular motion. A ball is tethered to
a rotational axis and is rotating counterclock-
wise around the specified path at a constant
angular rate ω. The velocity of the ball is a
vector tangential to the orbit, and is continu-
ously changing direction, a change requiring
a radially inward directed centripetal force.
The centripetal force is provided by the teth-
er, which is in a state of tension.
Centripetal force
is a force required to
make a body follow a curved path.[1] The
term centripetal force comes from the Latin
words centrum ("center") and petere ("tend
towards", "aim at"), signifying that the force
is directed inward toward the center of
curvature of the path. Isaac Newton’s de-
scription is found in the Principia.[2] Any
force (gravitational, electromagnetic, etc.) or
combination of forces can act to provide a
centripetal force. An example for the case of
uniform circular motion is shown in Figure 1.
Simple example: uniform
circular motion
The velocity vector is defined by the speed
and the direction of motion. Objects experi-
encing no net force do not accelerate and
hence move in a straight line with constant
speed;
they have a constant
velocity.
However, an object moving in a circle, even
at constant speed, has a changing direction
of motion. The rate of change of the object’s
velocity vector in this case is the centripetal
acceleration (see Figure 1).
The centripetal acceleration varies with
the radius of curvature of the path (R) and
speed (v) of the object, becoming larger for
greater speeds and smaller radii. If an object
is traveling in a circle with a varying speed,
its acceleration can be divided into two com-
ponents: a radial acceleration (the centripetal
acceleration that changes the direction of the
velocity) and a tangential acceleration that
changes the magnitude of the velocity.
The magnitude of the centripetal force is
given by:
where m is the mass, v is the magnitude of
the velocity, and r is the radius of curvatur