Circular Motion

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Circular Motion - PowerPoint PPT Presentation

Circular Motion. Evaluate, measure, and analyze circular motion. Analyze and evaluate the nature of centripetal forces. Investigate, evaluate and analyze the relationship among centripetal force, centripetal acceleration, mass, velocity, radius. Carousal.

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Circular Motion

Evaluate, measure, and analyze circular motion.

Analyze and evaluate the nature of centripetal forces.

Investigate, evaluate and analyze the relationship among centripetal force, centripetal acceleration, mass, velocity, radius.

Carousal
• Carousels are as reliant on the laws of motion as their more exciting cousins, the roller coasters.
• It's theoretically possible that, allowed to spin out of control, a carousel could gain enough speed so that the riders would be thrown off.
Carousal Continued…
• With all of its beauty and seeming simplicity, the carousel is a delicate balance of motion and forces.
• All of the horses move through one complete circle in the same amount of time.
• The horses on the outside of the carousel have to cover more distance than the inside horses in the same amount of time.
• This means the horses on the outside have a faster linear speed than those at the hub.
Carousal (galloping horses)
• On some carousels, the horses go up and down in a galloping motion simulating what it might be like to ride a real horse.
• In a normal carousel, each horse maintains a constant acceleration, radius, and tangential speed (speed tangent to the circular path of the carousel).
• If you add a gallop to some of the horses, you must consider the forces needed to change that horse's position upward or downward as it goes around the track.
• In designing with these forces in mind, you also need to take into account the mass of the horse and its rider.
• How do you tell the lead horse on a carousel?
• According to carousel legend, the lead horse of any carousel is always the biggest, most decorative horse.
• In many instances, this horse is a military or war horse.
• If a chariot is included in the carousel, the first horse right behind the chariot on the outside is the lead horse.
Circular Motion
• Kinematic concepts and motion principles will be applied to the motion of objects in circles and then extended to analyze the motion of such objects as roller coaster cars, a football player making a circular turn, and a planet orbiting the sun.

Uniform Circular Motion

Uniform Circular Motion
• The motion of an object in a circle with a constant or uniform speed.
• If you were driving a car at a constant speed and you were following the path of a perfect circle you would be experiencing uniform circular motion.
• An object moving in uniform circular motion would cover the same linear distance in each second of time.
Circular Motion
• The equation suggests that for objects moving around circles of different radius in the same period, the object traversing the circle of larger radius must be traveling with the greatest speed.
• In fact, the average speed and the radius of the circle are directly proportional.
Circular Motion
• A twofold increase in radius corresponds to a twofold increase in speed; a threefold increase in radius corresponds to a three--fold increase in speed; and so on.
Circular Motion
• If Uniform Motion means constant speed, does that also mean that it has constant velocity?
• Remember that velocity is a vector quantity as speed is a scalar quantity.
• A vector quantity has both magnitude and direction.
• The magnitude of velocity is simply the instantaneous speed of the object.
• The direction is directed in the same direction which the objects moves.
Circular Motion
• Since an object is moving in a circle, its direction is continuously changing.
• The best word that can be used to describe the direction of the velocity vector is the word tangential.
Circular Motion
• Does an object traveling in uniform circular motion have acceleration?
• Acceleration, like velocity, is a vector quantity and has both magnitude and direction.
• The magnitude is the change in speed over a given time.
• The direction will go in the direction of the object, just as it did with velocity.
• A change in either the magnitude or the direction constitutes a change in the velocity.
Circular Motion (Candle Demo)
• The flame deflects from its upright position, which signifies that there is an acceleration when the flame moves in a circular path at constant speed.
• A careful examination of the flame reveals that the flame will point towards the center of the circle, thus indicating that not only is there an acceleration; but that there is an inward acceleration.
• Objects moving in a circle at a constant speed experience an acceleration which is directed towards the center of the circle.
Circular Motion

Which of the following shows acceleration?

a.

d.

b.

e.

c.

Circular Motion (test knowledge)

Explain the connection between your answers to the above questions and the reasoning used to explain why an object moving in a circle at constant speed can be said to experience an acceleration.

Dizzy Smith and Hector Vector are still discussing #1e. Dizzy says that the ball is not accelerating because its velocity is not changing. Hector says that since the ball has changed its direction, there is an acceleration. Who do you agree with? Argue a position by explaining the discrepancy in the other student's argument.

Identify the three controls on an automobile which allow the car to be accelerated.

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.

Which vector below represents the direction of the velocity vector when the object is located at point B on the circle?

Which vector below represents the direction of the acceleration vector when the object is located at point C on the circle?

Which vector below represents the direction of the velocity vector when the object is located at point C on the circle?

Which vector below represents the direction of the acceleration vector when the object is located at point A on the circle?

Centripetal Force

Centripetal Force
• Law of Inertia (Newton’s 1st Law)
• "... objects in motion tend to stay in motion with the same speed and the same direction unless acted upon by an unbalanced force.“
• 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.

During the turn, the car travels in a circular-type path; that is, the car sweeps out one- quarter of a circle.

• 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 however is in motion and tends to stay in motion. It is the inertia of your body - the tendency to resist acceleration

This phenomenon might cause you to think that you were being accelerated outwards away from the center of the circle.

• 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.
Centripetal Force
• Any object moving in a circle (or along a circular path) experiences a centripetal force.
• 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 which moves in the circle.
Examples of Centripetal Force

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.

Check Understanding

An object is moving in a clockwise direction around a circle at constant speed. Use your understanding of the concepts of velocity, acceleration and force to answer the next five questions. Use the diagram shown at the right. Click the button to check your answers.

Which vector below represents the direction of the force vector when the object is located at point A on the circle?

Which vector below represents the direction of the force vector when the object is located at point C on the circle?

Which vector below represents the direction of the velocity vector when the object is located at point B on the circle?

Which vector below represents the direction of the velocity vector when the object is located at point C on the circle?

Which vector below represents the direction of the acceleration vector when the object is located at point B on the circle?