# What is the relationship between centripetal force and centrifugal

### Centripetal Force And Centrifugal Force | avesisland.info

The magnitude of the centripetal force, Fc, required to cause an object of mass m and speed v to travel in a circular path of radius r is given by the relation -. centripetal force and centrifugal force, action-reaction force pair associated with circular motion. According to Newton's first law of motion, a moving body travels . A centripetal force is a force that makes a body follow a curved path. Its direction is always The magnitude of the centripetal force on an object of mass m moving at The inverse relationship with the radius of curvature shows that half the time a particular radius of curvature applies, the centrifugal and Euler forces can.

There is only centripetal inward force and the inertia that makes objects in rotation under certain situations move outward, for example, a car making a turn, the movement of a roller coaster—even the spinning of a centrifuge. Consider an object in uniform circular motion: The formula for speed—or rather, average speed—is distance divided by time; hence, people say, for instance, "miles or kilometers per hour.

Furthermore, we can see that there is a proportional relationship between radius and average speed. If the radius of a circle is doubled, but an object at the circle's periphery makes one complete revolution in the same amount of time as before, this means that the average speed has doubled as well. This can be shown by setting up two circles, one with a radius of 2, the other with a radius of 4, and using some arbitrary period of time—say, 2 seconds.

The above conclusion carries with it an interesting implication with regard to speeds at different points along the radius of a circle.

Rather than comparing two points moving around the circumferences of two different circles—one twice as big as the other—in the same period of time, these two points could be on the same circle: Assuming they both traveled a complete circle in the same period of time, the proportional relationship described earlier would apply. This means, then, that the further out on the circle one goes, the greater the average speed. For an object in circular motion, the direction of velocity is the same as that in which the object is moving at any given point.

Consider the example of the city of AtlantaGeorgiaand Interstate, one of several instances in which a city is surrounded by a "loop" highway. Local traffic reporters avoid giving mere directional coordinates for spots on that highway for instance, "southbound on "because the area where traffic moves south depends on whether one is moving clockwise or counterclockwise.

### Centripetal force - Wikipedia

Hence, reporters usually say "southbound on the outer loop. The direction of the individual velocity vector at any given point may be described as tangential; that is, describing a tangent, or a line that touches the circle at just one point. By definition, a tangent line cannot intersect the circle.

• CENTRIPETAL FORCE
• Centrifugal Force vs. Centripetal Force
• Centrifugal force

It follows, then, that the direction of an object in movement around a circle is changing; hence, its velocity is also changing—and this in turn means that it is experiencing acceleration. As with the subject of centripetal force and "centrifugal force," most people have a mistaken view of acceleration, believing that it refers only to an increase in speed. In fact, acceleration is a change in velocity, and can thus refer either to a change in speed or direction.

Nor must that change be a positive one; in other words, an object undergoing a reduction in speed is also experiencing acceleration.

The acceleration of an object in rotational motion is always toward the center of the circle. This may appear to go against common sense, which should indicate that acceleration moves in the same direction as velocity, but it can, in fact, be proven in a number of ways.

### Centrifugal force - Wikipedia

One method would be by the addition of vectors, but a "hands-on" demonstration may be more enlightening than an abstract geometrical proof. It is possible to make a simple accelerometer, a device for measuring acceleration, with a lit candle inside a glass. When you hold the candle level, the flame points upward; but if you spin the glass in a circle, the flame will point toward the center of that circle—in the direction of acceleration.

The proof for this assertion lies in the second law of motion, which defines force as the product of mass and acceleration: Force is always in the direction of acceleration, and therefore the force is directed toward the center of the circle. In the above paragraph, we assumed the existence of mass, since all along the discussion has concerned an object spinning around a circle. By definition, an object—that is, an item of matter, rather than an imaginary point—possesses mass.

Mass is a measure of inertia, which can be explained by the first law of motion: This tendency to maintain velocity is inertia. Put another way, it is inertia that causes an object standing still to remain motionless, and likewise, it is inertia which dictates that a moving object will "try" to keep moving.

Centripetal Force Now that we have established the existence of a force in rotational motion, it is possible to give it a name: This is not a "new" kind of force; it is merely force as applied in circular or rotational motion, and it is absolutely essential.

Hence, physicists speak of a "centripetal force requirement": Instead, it will move in a straight line. The Latin roots of centripetal together mean "seeking the center. It would be correct to say that there is such a thing as centrifugal motion; but centrifugal force is quite a different matter. The difference between centripetal force and a mere centrifugal tendency—a result of inertia rather than of force—can be explained by referring to a familiar example.

Likewise, if the car stops suddenly, your body tends to move forward, in the direction of the dashboard. Note the language here: A car that is not moving is, by definition, at rest, and so is the rider. Once the car begins moving, thus experiencing a change in velocity, the rider's body still tends to remain in the fixed position. Hence, it is not a force that has pushed the rider backward against the seat; rather, force has pushed the car forward, and the seat moves up to meet the rider's back.

When stopping, once again, there is a sudden change in velocity from a certain value down to zero. In order to keep the stone moving in a circular path, a centripetal forcein this case provided by the string, must be continuously applied to the stone. As soon as it is removed for example if the string breaks the stone moves in a straight line.

In this inertial frame, the concept of centrifugal force is not required as all motion can be properly described using only real forces and Newton's laws of motion. In a frame of reference rotating with the stone around the same axis as the stone, the stone is stationary. However, the force applied by the string is still acting on the stone. If one were to apply Newton's laws in their usual inertial frame form, one would conclude that the stone should accelerate in the direction of the net applied force—towards the axis of rotation—which it does not do.

The centrifugal force and other fictitious forces must be included along with the real forces in order to apply Newton's laws of motion in the rotating frame. Earth[ edit ] The Earth constitutes a rotating reference frame because it rotates once a day on its axis.

## Difference Between Centripetal and Centrifugal Force

Because the rotation is slow, the fictitious forces it produces are small, and in everyday situations can generally be neglected. Even in calculations requiring high precision, the centrifugal force is generally not explicitly included, but rather lumped in with the gravitational force: Weight of an object at the poles and on the equator[ edit ] If an object is weighed with a simple spring balance at one of the Earth's poles, there are two forces acting on the object: Since the object is stationary and not accelerating, there is no net force acting on the object and the force from the spring is equal in magnitude to the force of gravity on the object.

In this case, the balance shows the value of the force of gravity on the object. When the same object is weighed on the equatorthe same two real forces act upon the object.

However, the object is moving in a circular path as the Earth rotates and therefore experiencing a centripetal acceleration. When considered in an inertial frame that is to say, one that is not rotating with the Earththe non-zero acceleration means that force of gravity will not balance with the force from the spring.

In order to have a net centripetal force, the magnitude of the restoring force of the spring must be less than the magnitude of force of gravity.

A major difference between centrifugal and centripetal force is the direction of each. Centrifugal takes place along the radius of the circle from the center out towards the object.

For centripetal, it is the opposite, taking place also along the radius of the circle, but from the object in towards the center. Basically, both are defined by their frame of reference, centrifugal from the center towards the outside, centripetal from the outside towards the inside or center. A couple examples of each type of force may help one see the difference between the two. A centrifugal force example is the mud flying off of a spinning tire, or children being pushed out on a merry-go-round.

The force the children feel is centrifugal force pushing them outward. A common example for centripetal force is the moon or a manmade satellite orbiting the Earth. The force comes from gravity, and is the same force allowing the planets to orbit the Sun.

If an object was being swung around on a rope the centripetal force is the tension in the rope.