# Centripetal force and mass relationship

### Centripetal force and gravitation | Physics | Science | Khan Academy

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. This implies that for a given mass and velocity, a large centripetal force Now we have a relationship between centripetal force and the coefficient of friction. This is sometimes referred to as the centripetal force requirement. The word centripetal (not to be confused with the F-word centrifugal) means center seeking.

These two driving scenarios are summarized by the following graphic.

### Centripetal force - Wikipedia

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.

12. Centripetal and Tangential acceleration - Hindi

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.

## The Centripetal Force Requirement

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.

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. It isn't a real force, but an apparent one.

The force you used with your hands to stay on the ride is real, and it is called centripetal force. Let's learn more about it.

Centripetal force is a force on an object directed to the center of a circular path that keeps the object on the path. Its value is based on three factors: Centrifugal force, on the other hand, is not a force, but a tendency for an object to leave the circular path and fly off in a straight line. Sometimes people mistakenly say 'centrifugal force' when they mean 'centripetal force. An object on a circular path In this diagram, centripetal force f is shown as a red arrow.

It is constant in magnitude but keeps changing direction so that it is always pointing to the center. Also shown on the diagram is the tangential velocity, v. Finally, the constant distance of the object from the center of the circle is represented by the variable r, or radius. How to Calculate Centripetal Force Centripetal force is easily calculated as long as you know the mass, m, of the object; its distance, r, from the center; and the tangential velocity, v. This equation is based on the metric system; note that the centripetal force, f, is measured in Newtons.

One Newton is approximately 0. There are some interesting things about this equation. Because the tangential velocity is squared, if you double the velocity you quadruple the centripetal force! Also, because r appears in the denominator, the magnitude of centrifugal force decreases as the object gets further away from the center. Finally, if you know the centripetal force, this equation can be rearranged to solve for velocity: Example Let's look at an example.

## Centripetal force

Suppose in our merry-go-round scenario Erica is standing at the edge of the ride holding onto the bars. Erica weighs 70 pounds. The diameter of the merry-go-round is 3 meters. The ride is making one complete revolution every 4 seconds. What is the centripetal force Erica must exert to hold onto the ride?