Application to

Circular Motion

Centrifugal Force

When the particle is stationary in the rotating reference frame (i.e., the particle's motion describes a circle of radius r and has angular velocity w in the inertial reference frame), the centrifugal force term, - m w x (w x r), reduces to + m vi2/r. The direction of the force points outward, away from the center of the circle. Since the particle is stationary in the rotating frame, vr, ar, the Coriolis force, and Feff are zero. Newton's second law in the rotating reference frame is then

Fi + m vi2/r = 0.

In the case of a car going around a circular curve, Fi is the force exerted by friction on the tires and points toward the center of the circular path (its value is negative), while m vi2/r is the centrifugal force and points outward, away from the center of the circular path. The two forces are equal in magnitude, but act in opposite directions. Hence, the net force on the particle in the rotating reference frame is zero.

In the case of circular planetary motion, Fi is the gravitational force exerted by the Sun on the planet, - GMm/r2, and points toward the Sun (G is the gravitational constant and equals 6.67×10-11 m3/(kg sec2), M is the Sun's mass, m the planet's mass, r the planet's orbital radius). m vi2/r is the centrifugal force and points away from the Sun. Newton's second law in the frame rotating with the planet's revolution and centered on the Sun is

- GMm/r2 + m vi2/r = 0.