Circular Motion - Detailed Help

Assignment CG4: The Centripetal Force Requirement

Objectives:
  • The student should be able to use the centripetal force requirement to identify the force which act centripetally in order to cause an object to move in circular motion.
  • The student should be able to analyze a physical situation involving circular motion and compare the magnitude of the individual forces which act upon an object.

 

Reading:

The Physics Classroom - Circular Motion Unit, Lesson 1, Part c

 

 

An object is moving in a circle at a constant speed in a 'clockwise fashion.' A 'God's eye' view of the circle is shown. For the indicated position, the direction of the velocity vector is represented by arrow ____; the direction of the acceleration vector is represented by ____; and the direction of the net force vector is represented by arrow ____.


The diagram uses a large dot to represent a specific location along a circle about which an object is moving. You are to pick three arrows which represent the directions of the velocity, acceleration and net force vectors at this location. Use the information in the Physics Rules sections below to complete this question.


Uniform Circular Motion and Velocity:

Velocity is a vector and has a direction. The direction of an object's velocity is always in the same direction that the object is moving. For an object moving in a circle at constant speed, the velocity vector is always directed in a direction which is tangent to the circle.


Uniform Circular Motion and Acceleration:

Accelerating objects are changing their velocity - either the magnitude or the direction of the velocity. Objects moving in a circle at a constant speed are accelerating due to their changing direction. The direction of the acceleration is directed toward the center of the circle about which the object moves. Such a direction is described as being centripetal.


Uniform Circular Motion and Net Force:

An object which moves in a circle is accelerating. Accelerations are caused by an unbalanced or net force. The net force is always in the same direction as the acceleration. For objects moving in circles at constant speed, the net force is directed towards the center of the circle about which the object moves. Such a direction is described as being centripetal.

For circular motion, what is the direction of the velocity vector?

For circular motion, what is the direction of the acceleration vector?

For circular motion, what is the direction of the net force vector?

 

 

A car is making a turn on a level roadway. The type of force which causes the car to make the turn is the ____.


Centripetal Force Requirement:

Circular motion requires an inward force. To travel along the curved path of a circle, there must be a force directed centripetally. Any object or thing could supply the force as long as it is directed toward the center of the circular path.


Think about this: When the steering wheel of a car is turned, the wheels of the car turn and the car's direction changes as it makes a turn. This almost always happens. But those of us who live in cold winter climates know that it doesn't always happen when there is ice, snow or slush on the road surface. Under such conditions, the steering wheel is turned and the tires are turned and the car continues in a straight line. So what force is present on the wheels of the car under dry conditions which is not present under icy conditions?


Often times, success in physics demands that you have the proper approach - a good game plan. When determining which type of forces supplies the centripetal force requirement, proceed through the list of forces and ask: Is this force present on the object? If yes, ask: In which direction does this force act? Answering these question demands that you understand each type of force. If necessary, use the link below to navigate to a web page which describes each force on the list of force types.


How are the various individual forces best described?

What is the direction of the net force for an object moving in a circle?

How do I know when a specific type of force is acting on an object?

 

 

An eraser is tied to a string and whirled in a horizontal circle at a constant speed. The type of force which causes the eraser to turn in a circle is the ____.


Centripetal Force Requirement:

Circular motion requires an inward force. To travel along the curved path of a circle, there must be a force directed centripetally. Any object or thing could supply the force as long as it is directed toward the center of the circular path.


Forces are not mysterious or ghostly. A force is simply a push or pull exerted upon an object as a result of its interaction with another object. The eraser is moving in a horizontal circle and there must be another object pushing or pulling on it towards the center of the circle. Make an effort to picture the situation and then ask; What physical object is directly interacting with the eraser to push or pull it toward the center of the circle? If necessary, use the Game Plan section below.


Often times, success in physics demands that you have the proper approach - a good game plan. When determining which type of forces supplies the centripetal force requirement, proceed through the list of forces and ask: Is this force present on the object? If yes, ask: In which direction does this force act? Answering these question demands that you understand each type of force. If necessary, use the link below to navigate to a web page which describes each force on the list of force types.


How are the various individual forces best described?

What is the direction of the net force for an object moving in a circle?

How do I know when a specific type of force is acting on an object?

 

 

Suppose that you're at an amusement park and you get on a barrel ride. You stand on a platform with your back to the barrel wall. The barrel spins rapidly in a circle, the platform is suddenly dropped out from under you, and you continue moving in a circle. The type of force which causes you to turn in a circle is the ____.


Centripetal Force Requirement:

Circular motion requires an inward force. To travel along the curved path of a circle, there must be a force directed centripetally. Any object or thing could supply the force as long as it is directed toward the center of the circular path.


Forces are not mysterious or ghostly. A force is simply a push or pull exerted upon an object as a result of its interaction with another object. If you are moving in a circle on a barrel ride, then there must be another object pushing or pulling on it towards the center of the barrel. Make an effort to picture the situation and then ask; What physical object would be interacting with me to push or pull me toward the center of the circle? If necessary, use the Game Plan section below.


Often times, success in physics demands that you have the proper approach - a good game plan. When determining which type of forces supplies the centripetal force requirement, proceed through the list of forces and ask: Is this force present on the object? If yes, ask: In which direction does this force act? Answering these question demands that you understand each type of force. If necessary, use the link below to navigate to a web page which describes each force on the list of force types.


How are the various individual forces best described?

What is the direction of the net force for an object moving in a circle?

How do I know when a specific type of force is acting on an object?

 

 

Suppose that you are on a roller coaster ride and are moving through a somewhat circular loop. You are at the bottom of the loop and have just begun the upward ascent through the loop (as pictured). One can conclude that the normal force acting upon your body is _____. List all that apply ... .


Centripetal Force Requirement:

Circular motion requires an inward force. To travel along the curved path of a circle, there must be a force directed centripetally. Any object or thing could supply the force as long as it is directed toward the center of the circular path.


At the bottom of a roller coaster loop, the passengers are entering a turn. They are beginning to move along a part of a circle (as pictured by the black dashed line) and they are at the bottom of that circle. The center of the circle is above the riders. There must be a net force directed toward this center in order to move along the turn. Think about how the normal force and the gravity force compare to each other in order to meet this centripetal force requirement. See Minds On Time section below.


You will need to find two answers which describe the normal force acting upon the riders. One answer will describe the direction and the other answer will describe the magnitude of the normal force. The normal force results from the contact between the riders and their seats. The seats are below the riders and push upward on the riders. This upward normal force must be sufficiently large to meet the centripetal force requirement. The net force must be upward (refer to Dig That Diagram section). The only other force acting upon the riders is gravity. Gravity acts downward and away from the center of the circle. In order to have a net upward (towards the center) force, the normal force must be bigger than the force of gravity.


What is the direction of the net force for an object moving in a circle?

What principles govern the relative size of individual forces for objects moving through roller coaster loops?

 

 

To the pleasure of the air show crowd, a pilot makes a series of loop-the-loops. At the bottom of one of the circular loops, the normal force on the pilot is ____. List all that apply ... .


Centripetal Force Requirement:

Circular motion requires an inward force. To travel along the curved path of a circle, there must be a force directed centripetally. Any object or thing could supply the force as long as it is directed toward the center of the circular path.


At the bottom of the loop-the-loop, the pilot is traveling along a circular path. The center of the circular path is above the pilot (as pictured). There must be a net force directed towards this center in order for the pilot to continue the circular motion. Think about how the normal force and the gravity force compare to each other in order to meet this centripetal force requirement. See Minds On Time section below.


You will need to find two answers which describe the normal force acting upon the pilot. One answer will describe the direction and the other answer will describe the magnitude of the normal force. The normal force results from the contact between the pilot and the seat. The seat is below the pilot and push upward on the pilot. This upward normal force must be sufficiently large to meet the centripetal force requirement. The net force must be upward (refer to Dig That Diagram section). The only other force acting upon the pilot is gravity. Gravity acts downward and away from the center of the circle. In order to have a net upward (toward the center) force, the normal force must be bigger than the force of gravity.


What is the direction of the net force for an object moving in a circle?

How do I know when a specific type of force is acting on an object?

What principles govern the relative size of individual forces for objects moving in a circle?

 

 

Suppose that you are on a roller coaster ride and are safely moving through a somewhat circular loop. You are at the top of the loop and riding along the inside of the loop (as pictured). One can conclude that the normal force acting upon your body is _____. List all that apply ... .


Centripetal Force Requirement:

Circular motion requires an inward force. To travel along the curved path of a circle, there must be a force directed centripetally. Any object or thing could supply the force as long as it is directed toward the center of the circular path.

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At the top of a roller coaster loop, the passengers are moving along a curved path. They are traveling along a part of a circle (as pictured by the black dashed line) and they are at the top of that circle. The center of the circle is below the riders. There must be a net force directed towards this center in order for the riders to continue along the turn. Constructing a free body diagram with the two individual forces shown will assist in answering this question. See Minds On Time section below.


You will need to find two answers which describe the normal force acting upon the riders. One answer will describe the direction and the other answer will describe the magnitude of the normal force. This is a unique situation in that the riders are upside down and the seats are above them. As such, the seats push downward on the riders. This means that there are two downward forces acting upon the riders at the top of the loop - gravity and normal force. The net force must be downward (refer to Dig That Diagram section). Since both individual forces are acting downward, the strength of the normal force will depend upon the acceleration. After all, gravity can supply as much as 9.8 m/s/s of downward acceleration. The normal force must supply the remaining force which is needed to sustain any acceleration greater than the gravitational value.


What is the direction of the net force for an object moving in a circle?

What principles govern the relative size of individual forces for objects moving through roller coaster loops?

 

 

A bucket of water is held by a rope and twirled in a vertical circle. The bucket is whirled more rapidly such that the speeds at both the top and the bottom of the circle are increased. As this increase in speed occurs, the _____. List all that apply ... .


Centripetal Force Requirement:

Circular motion requires an inward force. To travel along the curved path of a circle, there must be a force directed centripetally. Any object or thing could supply the force as long as it is directed toward the center of the circular path.


The acceleration (a) of an object moving in a circle is dependent upon the speed (v) of the object and the radius (R) of the circle. The relationship is expressed by the following equation.

a = v2 / R


Circular motion requires an inward force to cause the inward acceleration. The acceleration which is needed is dependent in part upon the speed of the bucket. Consistent with the equation in the Formula Fix section above, an increase in speed will cause the acceleration to increase. As would be reasoned from Newton's second law (Fnet = m•a), an increase in acceleration would require an increased net force. The net force is the vector sum of the two individual forces - gravity and tension. The force of gravity is dependent upon the object's mass and unaffected by a change in speed. Thus, the increased net force must result from an increase in the magnitude of the tension force.


What is the direction of the net force for an object moving in a circle?

How do I know when a specific type of force is acting on an object?

What principles govern the relative size of individual forces for objects moving in a circle?

 

 

A bucket of water is held by a rope and twirled in a vertical circle. The tension force acting upon the bucket would decrease to zero if ____.


Centripetal Force Requirement:

Circular motion requires an inward force. To travel along the curved path of a circle, there must be a force directed centripetally. Any object or thing could supply the force as long as it is directed toward the center of the circular path.


Give it a try (but not inside)! If you have a plastic bucket and a rope or heavy string, then you might give this one a try. Fill the bucket with an inch or two of water (more is not better), secure the rope or string to the bucket's handle and get ready to whirl. Go outside and find plenty of air space free from trees, windows, cars, streets, power lines and curious neighbors. With a quick burst of energy and a good grip on the string, begin spinning the bucket in a circle. Compare the tension in the string when the bucket is at the top and the bottom of the circular turn. Then gradually slow the bucket down over the course of several circles; observe the tightness of the string as the bucket approaches the top of the circle at this slower speed. What do you observe?


Circular motion requires an inward net force. At all points along the circle, the net force must be directed toward the center. The tension force is always inwards and gravity is always downwards. The downwards gravity force is towards the center of the circle when the bucket is at the top of the loop and away from the center of the circle when the bucket is at the bottom of the loop. At the top of the loop, both tension and gravity are directed towards the center. Together, these two forces supply provide sufficient force to sustain the acceleration experienced by the bucket at this location. Gravity can sustain an acceleration of 9.8 m/s/s. Whatever additional acceleration that there is must be sustained by the tension force. If the acceleration decreases to 9.8 m/s/s, then there will no longer be a tension force when the bucket is at the top of the loop. The bucket and the water would reach a free fall state in which the only force is gravity.


What is the direction of the net force for an object moving in a circle?

How do I know when a specific type of force is acting on an object?

What principles govern the relative size of individual forces for objects moving in a circle?