# What is the relationship between centripetal force and velocity

### The Centripetal Force Requirement

Note that the centripetal force is proportional to the square of the velocity, implying that a doubling of speed will require four times the centripetal force to keep. When an object is traveling in a circular path, centripetal force is what keeps it fixed in that path. but you were creating a balance between two forces - one real and Its value is based on three factors: 1) the velocity of the object as it . of Motion: Examples of the Relationship Between Two Forces And that tells us if the velocity speeds up the force will be stronger and the radius well be smaller. Only if the (linear) velocity remains the same.

Repeat the experiment for this radius. Be sure to indicate where the radius changes in your data table. If you have time, you might try to determine the relationship between mass and centripetal force.

In order to do this, you need to keep both the radius of the circle and the speed constant while you vary the mass and the centripetal force. You can design your own data table for this. You could also investigate the relationship between the radius and the centripetal force.

Calculate the period of revolution, T the time to go around once for each trial. Show a sample calculation. Calculate the linear speed, v, of the stopper for each trial.

### Physics Lab - Centripetal Force & Speed

Include a sample calculation. Theoretically, the centripetal force should be directly proportional to the square of the speed.

**11 chap 4 - Circular Motion 04 - Derivation of Centripetal Acceleration or Centripetal Force -**

To check this, add a column to your data table for v2. Construct a graph of centripetal force versus v2. Remember that it is customary to put the quantity you change force, in this case on the horizontal axis, and the quantity that changes by itself speed on the vertical axis. Be sure that you pick the largest convenient scale for your graph and draw the best smooth curve through your data points.

Is the graph of centripetal force versus speed squared a straight line? So, what can you say about the relationship between centripetal force and speed, then? 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.

## The Centripetal Force Requirement

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. The Centripetal Force and Direction Change 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.

## Circular Motion

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. As the centripetal force acts upon an object moving in a circle at constant speed, the force always acts inward as the velocity of the object is directed tangent to the circle.

This would mean that the force is always directed perpendicular to the direction that the object is being displaced.

The angle Theta in the above equation is 90 degrees and the cosine of 90 degrees is 0. Thus, the work done by the centripetal force in the case of uniform circular motion is 0 Joules. Recall also from Unit 5 of The Physics Classroom that when no work is done upon an object by external forces, the total mechanical energy potential energy plus kinetic energy of the object remains constant.

So if an object is moving in a horizontal circle at constant speed, the centripetal force does not do work and cannot alter the total mechanical energy of the object. For this reason, the kinetic energy and therefore, the speed of the object will remain constant. The force can indeed accelerate the object - by changing its direction - but it cannot change its speed.

In fact, whenever the unbalanced centripetal force acts perpendicular to the direction of motion, the speed of the object will remain constant. For an unbalanced force to change the speed of the object, there would have to be a component of force in the direction of or the opposite direction of the motion of the object. Applying Vector Components and Newton's Second Law A second approach to this question of why the centripetal force causes a direction change but not a speed change involves vector components and Newton's second law.

The following imaginary scenario will be used to help illustrate the point. Suppose at the local ice factory, a block of ice slides out of the freezer and a mechanical arm exerts a force to accelerate it across the icy, friction free surface.