5.16:
Centrifugal Force
Ever wondered why a ball flies outward in a rotating merry-go-round?
As the merry-go-round rotates, the ball traces a circular path. The component of the tension force in the string provides the necessary centripetal force for the circular motion of the ball.
The centripetal force is directed toward the center of the circle and is denoted by the product of the object's mass, the square of its angular velocity, and its distance from the axis of rotation.
Since the ball flies outward, it follows from Newton's third law that the inward centripetal force should have an equal and opposite outward reaction force. This outward force directed away from the center of rotation is called the centrifugal force.
The rotating ball in the merry-go-round experiences a centrifugal force that pushes it outward away from the center of rotation.
Centrifugal force is a pseudo force. It is considered only when the frame of observation is non-inertial.
5.16:
Centrifugal Force
Pseudo forces, or fictitious forces, appear to act on an object in motion in a rotating frame of reference with respect to an inertial reference frame. These forces are not real forces but rather mathematical constructs and are introduced to simplify calculations in a non-inertial frame while using Newton's laws of motion. Common examples of pseudo forces include centrifugal, Coriolis, and Euler forces. These forces are essential in fields such as mechanics, astrophysics, and fluid dynamics, where the motion of objects in non-inertial reference frames is commonly encountered.
Consider a ball tied to a string whirling in a horizontal plane. According to Newton's first law of motion, when observed from an inertial frame of reference, the ball would travel in a straight line. However, the tension in the string provides the centripetal force continuously to keep the ball moving in a circular path. Centrifugal force is not required in this inertial frame as all motion can be adequately described using only real forces and Newton's laws of motion.
Now, consider a frame of reference rotating with the ball around the same axis as the ball. As viewed from this frame, the ball is stationary. However, the tension force in the string or the centripetal force still acts on the ball directed towards the axis of rotation.
This contradicts Newton's laws of motion, according to which the ball must accelerate in the direction of the net applied force, i.e., towards the axis of rotation. Introducing a centrifugal force equal to and opposite to the centripetal force solves the problem. The net force on the ball is zero, which keeps it stationary in the rotating frame of reference.
Fictitious forces are necessary for formulating correct equations of motion using Newton's first two laws. However, the fictitious forces do not obey Newton's third law, which requires that the equal and opposite forces exist in the same frame of reference. This means that centrifugal and centripetal forces are not action and reaction forces.
Suggested Reading
- Giancoli, D.C (2014). Physics Principles with Applications. San Francisco, CA: Pearson. Appendix C.
- OpenStax. (2019). University Physics Vol. 1. [Web version] pp.298. Retrieved from https://openstax.org/books/university-physics-volume-1/pages/6-3-centripetal-force