Help me explain the difference between centripital and centrifugal forces?

Question

thanks in advance..

Answer 1

Both the terms are coming in circular motion. When a mass is moving in a circular path it will be under two forces. One is the centripetal force- a force which pulls the body towards the centre of the cicular path. Another one is its tendency to fly away from the centre.- centrifugal force. If both are balanced the body will remain in the circular path.
If a mass is whirled round with a string , the tension on the string is the force which pulls the body towards the centre. But due to its centrifugal force the tension on the string is balanced. During the whirl if the string happens to break the body will fly away tangentially.That means the centrifugal force has overcome the centripetal force.
The centrifugal force can be calculated by the formula:
(mv² / r). ie the force is directly proportional to the mass, and square of the velocity and inversely proportional to the radius of the circular path.
In the case of the satellites revolving round the earth the centrifugal force is the force due to its mass, velocity and the radius of the orbit(distance between the satellite and the centre of the earth.) This centrifugal force is balanced by the gravitational pull of the earth. The velocity at which the centrifugal force exceeds the gravitational pull is called the escape velocity.

Answer 2

The simple answer is...direction is the difference.

Centripetal force P = F centrifugal force in vector notation. This means P - F = 0 because P and F are the same magnitude (say, p and f) but they are pointed in the opposite directions (say, theta and theta+ 180 deg).

Vectors are simply values that have both magnitude and direction. Like, you're speeding along in your Ferrari at 120 kph, that's magnitude, which we sometimes call speed. It has no direction. But if we say, you're going 120 kph south towards Canne, that's a vector because it has both magnitude (120 kph) and direction (south or, conventionally, 180 deg).

Centripetal force P = p i-hat; where the i-hat is the so-called unit vector pointing in a direction along the radius of turn towards the axis of the turn. Think of i-hat as like a spoke on a turning wheel and i-hat > 0 when pointing inward to the axis and < 0 when pointing outward. p is the magnitude of P.

Centrifugal force F = f -(i-hat); where the negative sign in front of i-hat means that i-hat + -(i-hat) = 0 That is, whatever direction i-hat is, negative i-hat is in the opposite direction. And since each is a "unit" vector, meaning they have a magnitude of exactly one, they cancel each other out.

The laws of physics demand that P = p i-hat = f i-hat = F; or rewritten, p i-hat + f -(i-hat) = P - F = 0. But the only way that can happen each and every time is for p = f; the respective magnitudes must be equal even though their directions are opposites. Therefore p i-hat + p -(i-hat) = p (i-hat - i-hat) = p*0 = 0, which clearly shows that the only difference between centripetal and cetrifugal forces (at the same point) is their directions.

The reason the laws of physics demand that p = f and that their directions be in the opposite directions is because of good old f = ma...one of Newton's three laws. If P<>F, we'd have f = mA = P - F <> 0; where f is the net force (a vector) acting on a point that is rotating around an axis, like a point on that wheel with spokes.

As you can see, if f = mA <> 0; then A <> 0, where A is the acceleration of that point along the spokes of that wheel. That acceleration is along the spokes because the forces (P and F) are along the direction of the spokes (the radii of the rotation). In other words A = a i-hat or a -(i-hat) depending on the magnitudes p and f. If p > f, then i-hat is inward pointing; if p < f, then i-hat is outward pointing.

But, and this is a big BUT, if A <> 0, that would mean the point on the rim of the wheel would be accelerating inward or outward, depending on the magnitudes of the two forces P and F. That would be disasterous, your bicycle wheel and anything else solid and rotating would fly apart if the two forces did not offset each other. The point is, f = mA = 0 = P - F; so that P = F is a must or there would be no wheels, no satellites orbiting Earth, and so on. And this illustrates yet another of Newton's laws...for every force there is an equal, but opposite force (if there is no acceleration).

There is an equation that all first-year physics students learn for centrifugal force F = mv^2/R; where v = the tangential velocity (not the radial velocity) of the point R distance (e.g., the spoke length) from the axis of rotation (e.g., the hub of the wheel). If you examine the units, you can see that a = v^2/R; where A = a -(i-hat), which is the acceleration outward along the direction of R, the radius of rotation.

There is no similar equation for centripetal force P. But we don't need one because P = F = mv^2/R = mA. Thus, when we calculate F, we also get the value of P...a sort of two-fer.

One last point...some physicists claim centrifugal force is not a real force; it is only a force reacting to the real force, which is centripetal force. They argue, using our wheel example, that the spokes are the real source of the force that keeps the rim of the wheel turning in a circular path. In a satellite, gravity serves the same purpose of the spokes by keeping the satellites revolving in a (more or less) circular path around Earth. But, as the rim of the wheel or the satellites are not accelerating inward toward the hub or the center of the Earth, there is a reactionary force we call centrifugal force.

Sorry about the lesson in vectors, but when the only real difference is direction, vectors are the best way to explain that difference.

Answer 3

Whenever a body is in motion with uniform velocity ( constant speed and same direction ) and it is to be made to move on a circular path with constant speed, then its velocity has to be changed meaning the direction has to be changed. In order to achieve this a center-seeking force of constant magnitude but direction changing in such a way that it is always towards the center of the circular path has to be applied. Such a force is called centripetal force.

Centrifugal force is not real. It does not exist. That is why it is called a pseudo force. But the concept of centrifugal force is introduced to fit into equilibrium of statics which in this case is imaginary ( pseudo). Really, the body is not at all in static equilibrium, but is imagined to be in equilibrium in the radial direction. As the body moving on a circular path is not going nearer to the center nor away from it, it is said to be stationary in the radial direction. This is considered as a static equilibrium in the radial direction. But the radial direction of equilibrium itself is rotating. So it is a pseudo equilibrium. A body like a satellite revolving round a planet is being acted upon by the centripetal force, the source of which is the gravitational force of attraction which makes it move on a circular path. A centrifugal force equal to this centripetal force is considered to balance this centripetal force giving it a pseudo equilibrium in the radial direction.

Note:

I do not agree with eyeonthescreen that centrifugal force is a reactive force. It is not any force at all. There does not exist any real force by that name. In fact, there is no need to consider centrifugal force in analyzing a problem of classical mechanics, but it is usually done for simplification.

I read answer of Joyettan and am surprised to find that the misconception that the centrifugal force is a real force is quite wide spread. To further support my answer, I attach here in the source list three links which clarify how centrifugal force is a pseudo force.