basic science: circular motion

Circular Motion


Rotation Vs. Revolution

Reasons for Seasons

Because the Earth is tilted on its internal axis, as the Earth rotates tropical areas (close to Equator) receive direct sun rays. If the northern hemisphere of the Earth is tilted away from the sun, then it will receive indirect sun rays and will be cooler.....winter.

As Earth, which is tilted about its internal axis of rotation, revolves around the Sun (external axis of revolution of the Earth) seasons are changed.

Reason for Seasons explained link: Science U Website

Velocity Vectors in Circular Motion

Acceleration in Circular Motion

An accelerating object is an object which is changing its velocity. And since velocity is a vector which has both magnitude and direction, a change in either the magnitude or the direction constitutes a change in the velocity.

An object moving in a circle at constant speed is indeed accelerating. It is accelerating because its velocity is changing its directions.

Acceleration in Circular Motion

Acceleration is the rate at which velocity changes. vi represents the initial velocity and vf represents the final velocity after some time of t. The numerator of the equation is found by subtracting one vector (vi) from a second vector (vf).

The addition and subtraction of vectors from each other is done in a manner much different than the addition and subtraction of scalar quantities. Consider the case of an object moving in a circle about point C as shown in the diagram below. In a time of t seconds, the object has moved from point A to point B. In this time, the velocity has changed from vi to vf. The process of subtracting vi from vf is shown in the vector diagram; this process yields the change in velocity.

Note in the diagram below that there is a velocity change for an object moving in a circle with a constant speed. Furthermore, note that this velocity change vector is directed towards the center. An object moving in a circle at a constant speed from A to B experiences a velocity change and therefore an acceleration; this acceleration is directed towards point C - the center of the circle.

Velocity & Acceleration Vectors in Circular Motion

For questions #1-#4: An object is moving in a clockwise direction around a circle at constant speed. Use your understanding of the concepts of velocity and acceleration to answer the next four questions. Use the diagram shown at the right.
1. Which vector below represents the direction of the velocity vector when the object is located at point B on the circle?
2. Which vector below represents the direction of the acceleration vector when the object is located at point C on the circle?
3. Which vector below represents the direction of the velocity vector when the object is located at point C on the circle?
4. Which vector below represents the direction of the acceleration vector when the object is located at point A on the circle?
5. Make up your own questions.

Circular Motion on a level surface: 3 forces

A car moving in a horizontal circle on a level surface experiences 3 forces.
Applying the concept of a centripetal force requirement, we know that the net force acting upon the object is directed inwards.
	Since the car is positioned on the left side of the circle, the net force is directed rightward. An analysis of the situation would reveal that there are three forces acting upon the object - the force of gravity (acting downwards), the normal force of the pavement (acting upwards), and the force of friction (acting inwards or rightwards).
It is the friction force which supplies the centripetal force requirement for the car to move in a horizontal circle.
Without friction, the car would turn its wheels but would not move in a circle (as is the case on an icy surface).

The centripetal force (acting inwards) is the force of friction between the tires and the road

Centripetal Force Requirement An object moving in a circle is experiencing an acceleration. Even if moving around the perimeter of the circle with a constant speed, there is still a change in velocity and subsequently an acceleration. This acceleration is directed towards the center of the circle. And in accord with Newton's second law of motion, an object which experiences an acceleration must also be experiencing a net force; and the direction of the net force is in the same direction as the acceleration. So for an object moving in a circle, there must be an inward force acting upon it in order to cause its inward acceleration. 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. For object's moving in circular motion, there is a net force acting towards the center which causes the object to seek the center.

Without Centripetal Force	With Centripetal Force
Without a centripetal force, an object in motion continues along a straight line path.	With a centripetal force, an object in motion will be accelerated and change its direction.

According to Newton's first law of motion, it is the natural tendency of all moving objects to continue in motion in the same direction that they are moving ... unless some form of unbalanced force acts upon the object to deviate the its motion from its straight-line path. Objects will tend to naturally travel in straight lines; an unbalanced force is required to cause it to turn. The presence of the unbalanced force is required for objects to move in circles......unbalanced force is called.....centripetal force.

"Feeling Acceleration"

A Car Starts From Rest: You are a passenger in a stopped car. The drive "hits the gas". You "feel" as if you are moving (accelerating) backwards into the car seat.

As the wheels of the car spin to generate a forward force upon the car to cause a forward acceleration, your body tends to stay in place (Newton's 1st Law). It certainly might seem to you as though your body were experiencing a backwards force causing it to accelerate backwards; yet you would have a difficult time identifying such a backwards force on your body. Indeed there isn't one. The feeling of being thrown backwards is merely the tendency of your body to resist the acceleration and to remain in its state of rest. The car is accelerating out from under your body, leaving you with the false feeling of being thrown backwards.

A Car Traveling At A Constant Velocity In A Straight Line: Constant Motion: The driver hits the brakes. You "feel" as if you are moving (accelerating) forwards towards the dashboard.

Your body being in motion tends to continue in motion while the car is slowing to a stop. It certainly might seem to you as though your body were experiencing a forwards force causing it to accelerate forwards; 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.

In both scenarios: 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 (change in motion). The passengers lean is not an acceleration in itself but rather the tendency to maintain whatever state of motion they have while the car does the acceleration.

Centripetal Force

You are a passenger in a car making a left-hand turn on an off ramp maintaining a constant speed.

During the turn, the car travels in a circular-type path. The unbalanced force acting upon the turned wheels of the car cause 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 is in motion and tends to stay in motion. It is the inertia of your body - the tendency to resist acceleration - which 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 were 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.

Observe in the animation that the passenger (in blue) continues in a straight-line motion for a short period of time after the car begins to make its turn. In fact, the passenger follows a straight-line path until striking the shoulder of the driver (in red). Once striking the driver, a force is applied to the passenger to force the passenger to the right and thus complete the turn. An inward net force is required to make a turn in a circle. This inward net force requirement is known as a centripetal force requirement. In the absence of any net force, an object in motion (such as the passenger) continues in motion in a straight line at constant speed. This is Newton's first law of motion. While the car begins to make the turn, the passenger and the seat begin to edge rightward. As such, the car is beginning to slide out from under the passenger. Once striking the driver, the passenger can now turn with the car and experience some circle-like motion.

Centripetal Force Causes Circular Motion

As a car makes a turn, the force of friction acting upon the turned wheels of the car provide the centripetal force required for circular motion.	As a bucket of water is tied to a string and spun in a circle, the force of tension 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.

Circular Motion Lab

Centripetal Force

Centripetal force keeps the planets in orbit. According to Newton’s 1st law, all masses have inertia and would like to move at constant speed in a straight line. Earth wants to move straight but it is prevented from doing so due to the sun’s gravity. The sun applies a centripetal force.

When you spin a bucket of water over your head without spilling a drop, you are also applying a centripetal force. If you let go of the bucket, it will move in a straight line.

Centripetal force pulls the plane toward the center of the circle. The plane’s inertia makes it want to fly straight.

While the coaster cars zoom around the loop, the track exerts a centripetal force toward the center of the loop.

If you whirl a ball attached to string around your head, it moves in a circular path around you because the string is always pulling the ball directly toward the hand grabbing the string. The ball wants to move in a straight line and the string is pulling it directly inward. The resulting deflection is a compromise: a circular path. The string is applying a centripetal force to the ball: an inward force. If you let go of the string, there is no centripetal force and the ball will fly off in a straight line because of its inertia.

Roller Coaster G-Forces from The Physics Classroom

A coaster rider is continuously altering her direction of motion while moving through the loop; at all times, the direction of motion could be described as being tangent to the loop. This change in direction is caused by the presence of unbalanced forces and results in an acceleration. Not only is there an acceleration, the magnitude and direction of the acceleration is continuously changing.

To understand the feelings of weightlessness and heaviness experienced while riding through a loop, it is important to think about the forces acting upon the riders.

The only forces exerted upon the riders are the force of gravity and the normal force (the force of the seat pushing up on the rider). The force of gravity is at all times directed downwards and the normal force is at all times directed perpendicular to the seat of the car. Since the orientation of the car on the track is continuously changing, the normal force is continously changing its direction. The magnitude and direction of these two forces during the motion through the loop are depicted in the animation below.

In order for an object to move through a circle, it is necessary that there be a net inward force acting upon the rider. This is commonly referred to as the centripetal force requirement. Thus, the net force acting upon the rider is always directed inwards (towards the center of the circle). Since the net force is the vector sum of all the forces, the head-to-tail addition of the normal force and the gravity force should sum to a resultant force which is directed inward.

The diagram below depicts the free-body diagrams for a rider at four locations along the loop. The diagram also shows that the vector sum of the two forces (i.e., the net force) points towards the center of the loop for each of the locations.

Feelings of weightlessness and heaviness are associated with the normal force; they have little to do with the force of gravity. A person who feels weightless has not lost weight; the force of gravity acting upon the person is the same magnitude as it always is. Witness in the animation above that the force of gravity is everywhere the same. The normal force however has a small magnitude at the top of the loop (where the rider often feels weightless) and a large magnitude at the bottom of the loop (where the rider often feels heavy). The normal force is large at the bottom of the loop because in order for the net force to be directed inward, the normal force must be greater than the outward gravity force. At the top of the loop, the gravity force is directed inward and thus, there is no need for a large normal force in order to sustain the circular motion. The fact that a rider experiences a large force exerted by the seat upon her body when at the bottom of the loop is the explanation of why she feels heavy.