[Physics Class Notes] on Centripetal and Centrifugal Force Pdf for Exam

A force is a pull or push that acts on an object or a thing. Examples of force are gravitational force, frictional force, magnetic force, applied force etc. The force makes an object change its position, direction or speed. Newton (N) is the SI unit of force.

There are two ways to represent a force Balanced and Unbalanced Forces: 

• Balanced forces are forces acting on an object or a person from opposite directions that have equal force. These objects with balanced forces acting upon them will most likely be still such that they are not moving.

• Unbalanced forces are forces acting on an object or a person from opposite directions that are not equal. These objects with unbalanced forces acting upon them are in motion such that they are moving.

 

The Tug-of-War in the above image is a draw. No one is winning or losing, and they are called balanced forces. The Tug-Of-War in the above image shows the Left side winning because they have more force than on the right side and this is called an unbalanced force.

 

Now let’s discuss the three laws of force; Newton’s law of force will help us understand the following concept better.

 

Newton’s First Law of Motion

“Every object persists in its state of rest or uniform motion (moving) in a straight line unless it is compelled to change that state by forces executed on it.” Newton’s first law clearly states that every object will remain at rest or in uniform motion in a straight line unless compelled to change its state under the action of an external force. This is usually taken as the definition of inertia. The key ingredient is that if there is no net force (total force) acting on an object (if all the external forces cancel each other out), then the object will maintain a constant velocity. If that velocity is zero, then the object or a person remains at rest. When an external force is applied, the velocity will change because of the force.

 

 

Newton’s Second Law of Motion:

“The Force is equal to the change in momentum (motion of a moving body) per change in time. For a constant mass, force equals acceleration times the mass.”

The second law explains how the velocity of an object or a person changes when it is subjected to an external force. Newton also developed the calculus of mathematics, and the “changes” expressed in this law are most accurately defined in differential forms. (The Calculus can also be used to calculate the velocity experienced by an object subjected to an external force.) For an object with a constant mass m, the second law states that the force F is the product of an object’s mass (person’s mass) and its acceleration a:

 

 

F = ma, where F- force, m – the mass of the body, a- acceleration.

 

For an externally applied force, the change in velocity depends on the mass of the object. A force will cause a change in the velocity, and likewise, where there is a change in velocity will generate a force.

 

Let us take a case where a force applied to an object at rest causes it to accelerate in the direction of the force. However, if the object is already in motion, or if this situation is seen from a moving reference frame, that body might appear to slow down, speed up, or change its direction depending on the direction of the force, and the directions in which the object and reference frame is moving are relative to each other.

 

Newton’s Third Law of Motion:

 

Newton’s third law states that, for every action (force), there is an equal and opposite reaction (force). The third law states that for every action such that force in nature, there is an equal and opposite reaction. In other words, if an object, XYZ, exerts a force on object ABC, then object ABC also exerts an equal force on an object XYZ. Notice that these forces are exerted on different objects. The third law is the example of the generation of lift by a wing and the production of thrust by a jet engine. In the above figure, the balloon goes, and air goes down clearly explains the third law by showing every action has an equal and opposite reaction. With the above concepts, we have understood the basics required for centripetal force and centrifugal force.

 

Centripetal Force and Centrifugal Force:

 

The Latin word for centrifugal force is the center of Living. Centrifugal force is not really a force; it is rather a result of inertia. An object following a curved path to fly outwards away from the center of the curve is described by centrifugal force. Centripetal force counteracts the centrifugal force and prevents the object from “flying out” and instead keeps it moving at a uniform speed along a circular path.

Centrifugal force is present everywhere in our daily lives. We experience it when going around a corner in a car or when an airplane comes into a turn. We see it when the washing machine spins a cycle or when you take a ride on a merry-go-round. We never know; one day, it may even provide artificial gravity for spaceships and space stations.

 

Some people confuse centrifugal force with its counterpart, centripetal force, because they are so closely related. One might say they are two sides of a similar coin. Centripetal force is stated as, “The component of force acting on a body in curvilinear motion, directed toward the center of curvature or axis of rotation,” while centrifugal force is stated as, “The apparent force, equal and opposite to the centripetal force, pulling a rotating body away from the center of rotation, caused by the inertia of the body.”

 

Remember that while centripetal force is an actual force, centrifugal force is defined as an apparent force. In other words, when we twirl a mass on a string, the string exerts an inward centripetal force on the mass, while mass appears to exert an outward force on the string.

 

 

The above figure explains the centrifugal force and centripetal force when the car goes around the corner.

 

If you are observing and viewing a rotating system from the outside, you see an inward centripetal force acting to constraint the rotating body to a circular path. In the same way, if you are part of the rotating system, you experience an apparent centrifugal force that pushes you away from the center of the circle, even though what you are actually feeling is the inward centripetal force that keeps you from actually going off on a tangent.

 

The formula for both centrifugal and centripetal force is the same: F = ma = mv²/r. Where ac is the centripetal acceleration, m is the mass of the object, moving at velocity ‘v’ along a path with a radius of curvature (r).

 

Understanding and applying centrifugal and centripetal force is useful to many problems in our society. One example is related to the design of roads for the prevention of skidding and to improve traction on curves and access ramps of highways. The forces also were priceless for the invention of the centrifuge. The centrifuge is used to separate particles suspended in a fluid by spinning the test tubes at higher speeds.

 

We can say that “These forces are in different directions such that they are in the opposite direction because they undergo distinctive frames of reference. Even though these forces are really exact similar forces,” This brings us to Newton’s Third Law, which defines, “For every action, there is an equal and opposite reaction.” Just as gravity begins to exert a force on the ground, the ground appears to give out an equal and opposite force on your feet. When you are in an accelerating car, the seat exerts a forward force (motion) on you just as you appear to exert a backward force on the seat. In this case of a rotating system, the centripetal force pulls the mass inside to follow a curved path, while the mass appears to push outward due to its inertia. In each of these events, though, there is only one true force being applied, while the other is only an apparent force.

 

Formula

Both of  these forces can be calculated by using the same formula:

F=ma=mv²/r

Where m is the mass of the object which moves at velocity v along a path with a radius of the curvature, and ac is the centripetal acceleration.

Differentiation Between Centripetal Force and Centrifugal Force: