Why is centripetal force important

In this case, with the merry-go-round not rotating, the ball goes straight across to the girl. No problem. Now suppose the merry-go-round is spinning. If the boy tries to roll the ball straight across to the girl, the ball will indeed still go in a straight line assume small frictional forces as seen from someone not on the merry-go-round. The ball will not make it to the girl because she will rotate out of the way.

The boy and girl sitting on the spinning merry-go-round will see the ball not moving in a straight line in their reference frame of the merry-go-round. Here are two diagrams that might help. The problem is with the boy and the girl on the merry-go-round.

They see the ball NOT going in a straight line. Since they understand force and motion, they are saying "hey - if it is not moving in a straight line, there must be a force on it". They make a good point. However, they are not in an inertial frame of reference. Their frame is actually accelerating because it is moving in a circle. In order for things to work out in a non-intertial frame, a force needs to be added a non-real force.

This force is the centrifugal force. The centrifugal force is the force non-real force that is needed to make things work as you would think in a reference frame that is accelerating.

But for various practical reasons, this is not done. What makes an object take a circular path instead of a straight line? For example, why does a satellite orbit the Earth in a curved path, and what keeps a car moving around a curved road even at what seems like impossibly high speeds in some cases?

A classic example is the tetherball set-up found on U. In theory, all objects with mass exert a gravitational force on other objects. But because this force is proportional to the mass of the object, in most cases it is negligible for example, the infinitesimally small upward gravitational pull of a feather on the Earth as it falls. But perhaps an easier way to view the interplay between friction and rotational motion is to imagine objects that are able to "stick" to the outside of a rotating wheel better than others can at a given angular velocity because of the greater friction between the surfaces of these objects, which remain in a circular path, and the wheel's surface.

The angular velocity of a point mass or object is completely independent of what else might be going on with that object, kinetically speaking, at that point. After all, angular velocity is the same for all points in a solid object, regardless of distance.

After all, something moving in a circle yet accelerating would simply have to break free of its path, all else held the same. The physics basics prevent this apparent quandary from being a real one.

You would be right to ask: "But if the object is accelerating toward the center, why doesn't it move that way? Even if that linear velocity is constant, its direction is always changing thus it must be experiencing acceleration, which is a change in velocity; both are vector quantities. The formula for centripetal acceleration is given by:. From Figure , we see that the vertical component of the normal force is.

Now we can combine these two equations to eliminate N and get an expression for. That is, roads must be steeply banked for high speeds and sharp curves. Friction helps, because it allows you to take the curve at greater or lower speed than if the curve were frictionless.

Note that. Curves on some test tracks and race courses, such as Daytona International Speedway in Florida, are very steeply banked. This banking, with the aid of tire friction and very stable car configurations, allows the curves to be taken at very high speed. To illustrate, calculate the speed at which a We first note that all terms in the expression for the ideal angle of a banked curve except for speed are known; thus, we need only rearrange it so that speed appears on the left-hand side and then substitute known quantities.

Tire friction enables a vehicle to take the curve at significantly higher speeds. Airplanes also make turns by banking. The lift force, due to the force of the air on the wing, acts at right angles to the wing. When the airplane banks, the pilot is obtaining greater lift than necessary for level flight.

The banking angle shown in Figure is given by. Compare the vector diagram with that shown in Figure. Join the ladybug in an exploration of rotational motion. Rotate the merry-go-round to change its angle or choose a constant angular velocity or angular acceleration. A circular motion requires a force, the so-called centripetal force, which is directed to the axis of rotation. This simplified model of a carousel demonstrates this force.

What do taking off in a jet airplane, turning a corner in a car, riding a merry-go-round, and the circular motion of a tropical cyclone have in common? When taking off in a jet, most people would agree it feels as if you are being pushed back into the seat as the airplane accelerates down the runway. Yet a physicist would say that you tend to remain stationary while the seat pushes forward on you. An even more common experience occurs when you make a tight curve in your car—say, to the right Figure.

You feel as if you are thrown that is, forced toward the left relative to the car. We can reconcile these points of view by examining the frames of reference used. Let us concentrate on people in a car.

Passengers instinctively use the car as a frame of reference, whereas a physicist might use Earth. The physicist might make this choice because Earth is nearly an inertial frame of reference, in which all forces have an identifiable physical origin. The car is a noninertial frame of reference because it is accelerated to the side.

The force to the left sensed by car passengers is an inertial force having no physical origin it is due purely to the inertia of the passenger, not to some physical cause such as tension, friction, or gravitation. The car, as well as the driver, is actually accelerating to the right. This inertial force is said to be an inertial force because it does not have a physical origin, such as gravity. A physicist will choose whatever reference frame is most convenient for the situation being analyzed.

Noninertial accelerated frames of reference are used when it is useful to do so. Different frames of reference must be considered in discussing the motion of an astronaut in a spacecraft traveling at speeds near the speed of light, as you will appreciate in the study of the special theory of relativity.

Let us now take a mental ride on a merry-go-round—specifically, a rapidly rotating playground merry-go-round Figure.

You take the merry-go-round to be your frame of reference because you rotate together. When rotating in that noninertial frame of reference, you feel an inertial force that tends to throw you off; this is often referred to as a centrifugal force not to be confused with centripetal force. Centrifugal force is a commonly used term, but it does not actually exist. You must hang on tightly to counteract your inertia which people often refer to as centrifugal force.

But the force you exert acts toward the center of the circle. This inertial effect, carrying you away from the center of rotation if there is no centripetal force to cause circular motion, is put to good use in centrifuges Figure. A centrifuge spins a sample very rapidly, as mentioned earlier in this chapter.

Viewed from the rotating frame of reference, the inertial force throws particles outward, hastening their sedimentation. The greater the angular velocity, the greater the centrifugal force. But what really happens is that the inertia of the particles carries them along a line tangent to the circle while the test tube is forced in a circular path by a centripetal force. Let us now consider what happens if something moves in a rotating frame of reference. For example, what if you slide a ball directly away from the center of the merry-go-round, as shown in Figure?

A person standing next to the merry-go-round sees the ball moving straight and the merry-go-round rotating underneath it. Up until now, we have considered Earth to be an inertial frame of reference with little or no worry about effects due to its rotation.

Yet such effects do exist—in the rotation of weather systems, for example. Viewed from above the North Pole, Earth rotates counterclockwise, as does the merry-go-round in Figure.

Just the opposite occurs in the Southern Hemisphere; there, the force is to the left. The Coriolis force causes hurricanes in the Northern Hemisphere to rotate in the counterclockwise direction, whereas tropical cyclones in the Southern Hemisphere rotate in the clockwise direction.

The terms hurricane, typhoon, and tropical storm are regionally specific names for cyclones, which are storm systems characterized by low pressure centers, strong winds, and heavy rains. Yet you would once more have a difficult time identifying such a forwards force on your body.

Indeed there is no physical object accelerating you forwards. The feeling of being thrown forwards is merely the tendency of your body to resist the deceleration and to remain in its state of forward motion. This is the second aspect of Newton's law of inertia - "an object in motion tends to stay in motion with the same speed and in the same direction You are once more left with the false feeling of being pushed in a direction which is opposite your acceleration.

In each case - the car starting from rest and the moving car braking to a stop - the direction which the passengers lean is opposite the direction of the acceleration. This is merely the result of the passenger's inertia - the tendency to resist acceleration. The passenger's lean is not an acceleration in itself but rather the tendency to maintain the state of motion while the car does the acceleration.

The tendency of a passenger's body to maintain its state of rest or motion while the surroundings the car accelerate is often misconstrued as an acceleration.

This becomes particularly problematic when we consider the third possible inertia experience of a passenger in a moving automobile - the left hand turn. Suppose that on the next part of your travels the driver of the car makes a sharp turn to the left at constant speed. During the turn, the car travels in a circular-type path. That is, the car sweeps out one-quarter of a circle.

The friction force acting upon the turned wheels of the car causes an unbalanced force upon the car and a subsequent acceleration. The unbalanced force and the acceleration are both directed towards the center of the circle about which the car is turning. Your body however is in motion and tends to stay in motion. It is the inertia of your body - the tendency to resist acceleration - that causes it to continue in its forward motion. While the car is accelerating inward, you continue in a straight line.

If you are sitting on the passenger side of the car, then eventually the outside door of the car will hit you as the car turns inward. This phenomenon might cause you to think that you are being accelerated outwards away from the center of the circle.

In reality, you are continuing in your straight-line inertial path tangent to the circle while the car is accelerating out from under you. The sensation of an outward force and an outward acceleration is a false sensation. There is no physical object capable of pushing you outwards. You are merely experiencing the tendency of your body to continue in its path tangent to the circular path along which the car is turning.

You are once more left with the false feeling of being pushed in a direction that is opposite your acceleration. Any object moving in a circle or along a circular path experiences a centripetal force. That is, there is some physical force pushing or pulling the object towards the center of the circle. This is the centripetal force requirement. The word centripetal is merely an adjective used to describe the direction of the force. We are not introducing a new type of force but rather describing the direction of the net force acting upon the object that moves in the circle.

Whatever the object, if it moves in a circle, there is some force acting upon it to cause it to deviate from its straight-line path, accelerate inwards and move along a circular path.

Three such examples of centripetal force are shown below. As a car makes a turn, the force of friction acting upon the turned wheels of the car provides centripetal force required for circular motion. As a bucket of water is tied to a string and spun in a circle, the tension force acting upon the bucket provides the centripetal force required for circular motion. As the moon orbits the Earth, the force of gravity acting upon the moon provides the centripetal force required for circular motion.

The centripetal force for uniform circular motion alters the direction of the object without altering its speed. The idea that an unbalanced force can change the direction of the velocity vector but not its magnitude may seem a bit strange. How could that be? There are a number of ways to approach this question. One approach involves to analyze the motion from a work-energy standpoint.

Recall from Unit 5 of The Physics Classroom that work is a force acting upon an object to cause a displacement.