I.
OBJECTIVES At the end of the lesson, the students should be able to: A. describe uniform circular motion and its parameters; B. differentiate speed, velocity, and acceleration; C. identify the things and events that exhibit uniform circular motion; and D. explain the relationship of Newton’s laws of motion to uniform circular motion.
II. SUBJECT MATTER A. TOPIC: Circular Motion B. SUBTOPIC: Uniform Circular Motion C. CONCEPTS: a) Circular motion is a movement of an object along the circumference of a circle or rotation along a circular path. It can be uniform with constant angular rate of rotation and constant speed, or non-uniform with changing rate of rotation. b) Uniform circular motion is the motion of an object traveling at a constant speed on a circular path. c) Uniform circular motion involves centripetal acceleration (center-pointing acceleration) and centripetal force (center-pointing force). D. SKILLS TO BE DEVELOPED: Explaining, identifying, describing, analyzing, and differentiating one parameter from the other. E. VALUES: The students will apply the Newton’s laws of motion in understanding the concept of uniform circular motion. The students will see the importance of understanding the concept of uniform circular motion to various laws of physics. F. MATERIALS USED: Laptop, LCD projector, board marker, and visual aid G. REFERENCES: Giancoli, Douglas C.,Physics(Fifth Edition).pp.112-115 www.m.sparknotes.com www.wedassign.net www.gktoday.in/uniform-circular-motion
III. LEARNING TASKS Teacher’s Activity
Students’ Activity
A. Preparation a) Review of the past lesson Last meeting we discussed about Newton’s laws of motion. Again who can enumerate those laws of motion? Yes, Gizel. The Newton’s laws of motion are the law of inertia, law of acceleration, and law of interaction. Exactly! Who can state the law of inertia? Yes, Christian. Law of inertia states that “a body at rest stays at rest, and a body in motion stays in motion at the same speed in a straight line unless acted upon by unbalanced force”. That’s right! What about the law of acceleration? Anyone? Yes, Girlie. Law of acceleration states that “the force is directly proportional to the acceleration and inversely proportional to its mass”. Very good! How about the law of interaction? Yes, Lyra. Law of interaction states that “in every action there’s an equal and opposite reaction”. Exactly! Class, familiarize yourselves with those laws of motion because those laws will guide you for better understanding the concept of our next topic. Did you understand? Yes Ma’am. Do you have any question? None Ma”am.
B. Motivation Before we start our discussion, let me ask you this question. Are you accelerating right now? Sitting there without changing your direction, do you think you are accelerating? Yes Ma’am. Why? Anyone who can justify your answer? Yes, Girlie. We are accelerating because our planet orbits the sun, therefore we are moving in a circle, but we are also spinning on the Earth’s axis, and I would say that we are definitely accelerating because if you are moving in a circle, uniform or non-uniform, you are in fact accelerating. Precisely! Let’s prove this as we go on to our discussion. C. Presentation Again, let me ask another question, have you tried to ride on a peris wheel? Yes Ma’am. While you were riding on the peris wheel, what have you noticed? Yes, Kate. I noticed that my speed remains constant but my direction is continuously changing. Very good! That will be related to our new topic which is the uniform circular motion. D. Lesson Proper What is uniform circular motion? Yes, Sv. Uniform circular motion is the motion of an object traveling at a constant (uniform) speed on a circular path. Okay. Thank you. An object that moves in a circle at
constant speed is said to experience uniform circular motion. The magnitude of the velocity remains constant in this case, but the direction of the velocity continuously changes as the object moves around the circle. When we say magnitude of the velocity and direction of the velocity, what does it mean? Yes, Rayma. When we say magnitude of the velocity, it is only referring to its speed while the direction of the velocity talks about the velocity itself. Precisely! So, based on what Rayma have said, will you differentiate speed from velocity? Yes, Marisa. Speed is just how fast you’re moving. Velocity on the other hand, is your speed and direction. Very good! Between the speed and velocity, where is the scalar and the vector quantity? Yes, King. Speed is the scalar quantity and velocity is the vector quantity. Exactly! How did you say that speed is scalar and velocity is vector? Will you cite an example? Yes, Lyra. Speed is scalar because it doesn’t have a direction, while velocity is vector because it does have a direction. For example, the speed of the car is 300 miles/hour, and its velocity is 300 miles/hour South. Very well said. Now, let’s talk about acceleration. What is acceleration? Yes, Reynald. Acceleration is a change in velocity. That’s right.
So how can something moving in a circle at constant speed have an acceleration? Yes, Kate. Since an object moving in a circle is constantly changing direction, its velocity is constantly changing. And whenever something’s velocity is changingeven if only its direction, not its speed, that object must be accelerating. Exactly! So its been proven that we are definitely accelerating because the Earth in which we live undergoes circular motion as it rotates on its axis and revolves around the sun. But why don’t we feel that we are accelerating? Anyone, who has an idea? Yes, Laudino. We don’t feel the we are accelerating because our Earth is very big. Very good! Class, do you have any question about the difference among speed, velocity, and acceleration? None Ma’am. If that’s the case, let’s proceed to centripetal acceleration or a so called center-pointing acceleration. For centripetal acceleration, we have the equation ; where a is the centripetal a 2) acceleration(m/s , v is the velocity(m/s), r is the radius(m). What does it mean? Yes, Hilario.
v2 r
and
Centripetal acceleration is directly proportional to velocity squared and inversely proportional to the radius. Very good! Take a look on this figure.
Which motion has the largest centripetal acceleration? Why? Yes, April. The motion in letter B because it has a large velocity and a small radius. Exactly! Circular motion also requires a net force, and this force is what we called centripetal force or center-pointing force. Is centripetal force considered a force created by nature? No Ma’am. That’s right! Centripetal force does not indicate some new kind of force created by nature. The term merely describes the direction of the net force needed to provide a circular path- that is toward the center. Newton’s second law indicates that whenever an object accelerates, there must be a net force to create the acceleration. What does this statement signifies to uniform circular motion? Yes, Aizah. In uniform circular motion, there must be a net force to produce the acceleration. A net force is necessary because otherwise, if no net force were exerted on the object, it would not move in a circle but in a straight line. Exactly! Consider this figure.
An object on a guideline is in uniform circular motion. The object is symbolized by a dot, and at point O, it is release suddenly from its circular path. If the guideline is cut suddenly, will the object move along OA or OP ? How ? Yes, Jenifer. The object will move along a straight line between point O and P, because according to Newton’s first law of motion “an object continues in a state of rest or in a state of motion at a constant speed along a straight line unless compelled by changes that state by a net force”. So, when the object is suddenly released from its circular path, there is no longer a net force being applied to it. As a result, the object would move along the straight line between points O and A, not on the circular arc between points O and P. Excellent! Did you get it class? Yes Ma’am. But there is a common misconception that an object moving in a circle has an outward force acting on it, a so-called centrifugal (center-fleeing) force. This is incorrect, there is no outward force on the revolving object. To prove this, may I have a volunteer here in front to do the task. Anyone? Yes, Hilario. I have here a ball suspended by the string. In order for a ball to move in a circular motion, continuously pull the string. (The student did the task.) The misconception arises when the “pull” is interpreted as an outward force pulling on the ball that is transmitted along the string to his hand. This is not what is happening at all. To keep the ball moving, again pull inwardly the string. The string exerts this force on the ball, and the ball exerts an equal and opposite force on the string. Class, in what law of motion would fall this situation?
Yes, Kate. That situation will fall under Newton’s third law of motion which is the law of interaction which states that in every action there is an equal and opposite reaction. Very good! The force on the ball is the one exerted inwardly on it by his hand, via the string. E. Valuing (Picture Analysis) Class, I have here pictures. What can you say about these pictures? Yes, Aizah. The pictures show different events or situations undergoing uniform circular motion. Precisely! These pictures show some events that exhibit uniform circular motion. Look at picture A, who can describe it? Yes, Ronalyn. Picture A shows a car on the road making a turn. Very good. What kind of force involved to this? Yes, Jerick. The force involved between the car and the road is a frictional force. Very good! How about the picture B, who will describe and tell what kind of force was involved? Yes, Stephen. Picture B shows a satellite revolving the Earth, and the force that involved with this is the gravitational force. Excellent! What about the third picture, will you describe and tell what kind of force was involved? Yes, Marisa. Picture B shows a man whirling a ball which is tied at the end of the string, and the force involved is the tension.
Exactly! These are some of the the events that undergoes uniform circular motion that we can observe in our daily lives, and understanding the concept of uniform circular motion helps us to explain various concepts of physics. Is it clear, class? Yes Ma’am. Do you have any question? None Ma’am. IV. EVALUATION Class, on the board are the terminologies involved in a uniform circular motion. Your task is to match those terms with their corresponding descriptions. TERMINOLOGY
VELOCITY SPEED
DESCRIPTION
Chance in velocity. Does not have a direction.
ACCELERATION
A force that involves on the string.
TENSION
Describes how fast the body moves.
FRICTIONAL FORCE
A force involves on a car on the road.
GRAVITATIONAL FORCE CENTRIPETAL ACCELERATION
A force involves between the Earth and the satellite. Does have a direction.
SCALAR QUANTITY
Center-pointing acceleration.
VECTOR QUANTITY
How fast the body moves with respect to its magnitude and direction,
V. AGREEMENT A. Give another 3 events or situations that exhibit uniform circular motion.
B. Read about Non-uniform Circular Motion and using a venn diagram, compare and contrast uniform from non-uniform circular motion. Reference: Physics by Douglas C. Giancoli. pp. 122-123
Republic of the Philippines ISABELA STATE UNIVERSITY San Mariano Campus Sta. Filomena, San Mariano, Isabela
A DEMONSTRATION PLAN IN PHYSICAL SCIENCE (Uniform Circular Motion)
Submitted by: NOVY-ANN U. SANCHO
Submitted to: CLARINA S. SARMIENTO, Ph.D. Program Chairman, Education Department
First Semester, S.Y. 2016-2017