Table of Contents
CENTRIFUGAL FORCE
The force of centrifugal force is an apparent force that affects objects in circular motion by pushing them away from the center of rotation. It is not a true force but rather a product of inertia experienced in a rotating frame of reference. When an object moves in a circle, its natural tendency to move in a straight line is counteracted by the centripetal force pulling it towards the center. The outward feeling experienced, such as on a spinning ride or in a turning vehicle, is what we identify as centrifugal force. It plays a crucial role in various applications, ranging from car dynamics to the design of space stations.
WHAT IS CENTRIFUGAL FORCE?
Let us assume that a swing rotating horizontally is at rest. A person is sitting on that swing and has a stone in his hand. Now, the pendulum began to rotate at right angles. As a result, the stone will also rotate with the person. Now, the following two observers will discuss the motion of the stone in two ways.
- A Spectator Standing Still on the Surface: As the stone rotates in a circle, this observer would say that a centripetal force is acting on the stone. Because we know, only when the centripetal force is active, it is possible for an object to move in a circle. If the person sitting on the swing releases the stone from his hand at point A, the observer will see the stone moving along the tangent (AB) to the circle. In that observer’s eyes the stone moves along the path AB due to inertia.
- Spectators Sitting on Swings: This observer is rotating with the same angular velocity as the stone. So, he always sees the stone in the same position relative to himself. That is, he will think that the stone is stationary. If this spectator releases the stone from his hand at point A, after some time when the stone reaches point B, the spectator swinging will also reach point C. So, in his eyes the motion of the stone will be along the centroidal line CB. It will appear to him that the stone is moving outwards along the radius of the circle under the influence of a force. This is centrifugal force.
Note that, given that point B or C is very close to point A, AB ≈ arc AC. To an observer standing still on the surface, i.e. in a fixed coordinate system, the centrifugal force does not exist, only in a rotating coordinate system. It is not a real force interacting between different objects. This is why it is called a pseudo force.
If the person sitting on the swing holds the stone with his hands, the stone cannot fall out. That is, the person applies a force on the rock with the hand. This real force (which is the real centripetal force to the eye of an observer standing still on the surface) and the imaginary centrifugal force keep the stone in equilibrium (relative to the person sitting on the swing). So, these two forces are equal and opposite to each other. So, if an object of mass m moves with velocity v (angular velocity ω) in a circle of radius r,
Centrifugal Force = mv²/r = mω²r
Definition: If an object rotates in a circular path with angular velocity and an observer moves along with the object with the same angular velocity, then the observer perceives that a force equal and opposite to the centripetal force is acting on the rotating object. That force is called centrifugal force.
SOME PRACTICAL EXAMPLES OF CENTRIFUGAL FORCE
The existence of centrifugal force due to rotational motion is understood in many cases of daily life. Let’s see some examples of them.
LOSS OF WEIGHT OF A BODY DUE TO THE DIURNAL MOTION
Earth rotates around its axis once every 24 hours. This is the diurnal motion of the earth. As a result of the Earth’s rotation about its axis, every object on the Earth’s surface rotates with the same angular velocity.
Let us assume that the latitude of point A on Earth is θ; there is an object of mass m at point A. The mass of the object mg acts along the line AO towards the center of the earth. Again, the diurnal motion of the earth causes the object to rotate in a circular path of radius r around the earth’s axis with an angular velocity ω and experiences an outward centrifugal force mω²r along BA. The component of this centrifugal force in AC direction is mω²rcosθ. As this fraction acts in the opposite direction to the weight mg, the object’s weight actually decreases slightly, i.e., the object’s apparent weight decreases. Note that if the Earth were stationary, there would be no centrifugal force, so the weight would not decrease.
Hence, the weight of the object at point A is,
W = mg – mω²rcosθ
= m (g – ω²rcosθ) [R is the radius of the earth and r = Rcosθ]
At the equator, θ = 0,
Therefore, W = m (g – ω²R)
Thus, the weight loss of objects in the equatorial region is greatest for the diurnal rotation of the Earth.
At pole θ = 90⁰, so W = mg
Hence, there is no loss of weight of a body in polar regions.
REASON FOR FLATTENING OF EARTH AT THE POLES
The shape of the earth is not perfectly round, but more like an orange, that is, the north and south polar regions are slightly depressed and the equatorial region is slightly inflated. The reason for this particular shape is the Earth’s daily motion around its axis and the resulting centrifugal force.
Earth was very hot when it was created. So basically, the Earth was made up of molten and gaseous matter. Centrifugal force is highest in the equatorial region, so the molten or gaseous particles located in the equatorial region at the beginning of creation had no tendency to move away from the axis under the influence of centrifugal force. But from the very beginning the mutual cohesive force of the particles mediated by the Earth was substantial. As a result, objects in the equatorial region moved slightly away from the axis due to the centrifugal force, while objects in the polar region moved slightly inward due to the cohesive force. Later, as the Earth cooled and solidified, this feature of the Earth’s shape remained. This is why the polar regions are slightly depressed and the equatorial region is slightly inflated.
DIFFERENCES BETWEEN CENTRIPETAL AND CENTRIFUGAL FORCE
| CENTRIPETAL FORCE | CENTRIFUGAL FORCE |
|---|---|
1. It is real force which is exerted on the body by the external agencies like gravitational force, tension in string, normal force etc. | 1. It is pseudo force or fictitious force which cannot arise from gravitational force. |
2. Acts both in inertial and non-inertial frame of references. | 2. Acts only in rotating frames (non-inertial frame). |
3. It acts towards the axis of rotation or centre of the circle in circular motion, Fcp = mω²r = mv²/r. | 3. IT acts outwards from the axis of rotation or radially outwards from centre of the circular motion, Fcf = mω²r = mv²/r. |
4. Real force and has real effects. | 4. Pseudo force but the has real effects. |
5. Origin of centripetal force is interaction between the objects. | 5. Origin of centrifugal force is inertia. It does not arise from interaction. |
6. In inertial frames centripetal force has to be included when free body diagram has drawn. | 6. In inertial frames there is no centrifugal force. In rotating frames both centripetal and centrifugal force have to be included when free body diagrams are drawn. |
CONCLUSION
To summarize, centrifugal force is an apparent force perceived in a rotating reference frame that acts outward away from the centre of rotation. Although not a real force in an inertial frame, it contributes to the illusion of being pushed outward when an item moves in a circular direction. This perceived force is due to inertia, as objects tend to move in a straight line until moved upon. Centrifugal force is vital for comprehending scenarios such as a car turning or water spinning out of clothes in a washing machine, emphasising its practical importance in everyday life.
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