Uniform circular motion (UCM) is the motion of an object in a perfect circle with a constant or uniform speed.

Size: px
Start display at page:

Download "Uniform circular motion (UCM) is the motion of an object in a perfect circle with a constant or uniform speed."

Transcription

1 Uniform circular motion (UCM) is the motion of an object in a perfect circle with a constant or uniform speed.

2 1. Distance around a circle? circumference 2. Distance from one side of circle to the opposite side which goes through the center of the circle diameter 3. Distance from center of the circle to any point on the edge of the circle radius 4. Is there an equation that relates the distance around a circle (circumference) to the radius of the circle? (C = 2πr)

3 The radian is a pure measure based on the radius of the circle: 5. radian: the angle made by taking the radius and wrapping it along the edge of a circle:

4 There are π radians in a half circle And also 180 in a half circle So π radians = 180 So 1 radian = 180 /π = 57.3 Imagine you cut up pieces of string exactly the length from the center of a circle to its edge how many pieces do you need to go around the edge of the circle? Answer: 2π (or about pieces of string).

5 # 6,7 & 8 = 1 rev = 360 Positive rotation is considered to be counterclockwise

6 9. Complete the following table # revolutions rads degrees π/2 π 270 1

7 9. Complete the following table # revolutions rads degrees 1/4 π/2 90 1/2 π 180 3/4 3/2π π 360

8 Linear Velocity Objects moving in a circle still have a linear velocity = distance/time. This is often called tangential velocity, since the direction of the linear velocity is tangent to the circle. v

9 10a. A car travels in perfectly circular motion. If the radius of the circle is 25m meters how far does the car travel if (C = 2πr) It goes completely around the circle? C = 2 π 25 = 157 m C = 2 π rads = 6.28 rads = b. It goes halfway around the circle? Halfway around is 78.5 meters or π rads = 3.14 rads = c. It goes one fourth of the way around the circle? 1/4 th of the way is 39.2 meters or π/2 rads = 1.57 rads = 90

10 11. What is the equation to find the speed of an object with uniform circular motion? Average speed (v) = distance = circumference time time circumference equals?? V = 2 π r T 12. T is the time for one revolution or one cycle. This quantity T is called the period!

11 13. If the radius of the circle is 6 meters, what is the average speed of a minion on a motorcycle traveling completely around a circle in 4 sec? V = 2 π r T V = 2 π 6m 4 sec = 9.42 m/s 14. How far around the circle in meters and degrees would the minion move in 2.5 seconds? d = vt (9.42 m/s) (2.5 sec) =? = 23.55m =? 2 π r (a bit more than halfway)

12 What if we do not know the radius of the circle but we know that the minion completes a revolution around a circle in 4 sec? 15. We can determine the angular velocity ω of the minion in rads/sec ω = 2 π rads T

13 What if we do not know the radius of the circle but we know that the minion completes a revolution around a circle in 4 sec? 15. We can determine the angular velocity ω of the minion in rads/sec ω = 2 π rads T ω = 2 π rads 4 sec = 1.57 rads/sec

14 What if we do not know the radius of the circle but we know that the minion completes a revolution around a circle in 4 sec? 15. We can determine the angular velocity ω of the minion in rads/sec ω = 2 π rads T ω = 2 π rads 4 sec = 1.57 rads/sec 16. How far around the circle in rads would the minion move in 2.5 seconds? θ= ωt where θ = angular displacement in rads (θ is theta)

15 What if we do not know the radius of the circle but we know that the minion completes a revolution around a circle in 4 sec? 15. We can determine the angular velocity ω of the minion in rads/sec ω = 2 π rads T ω = 2 π rads 4 sec = 1.57 rads/sec 16. How far around the circle in rads would the minion move in 2.5 seconds? θ= ωt where θ = angular displacement in rads (θ is theta) θ = 1.57 rads/sec) (2.5 sec) =? = 3.9 rads 17. How many degrees is this?

16 What if we do not know the radius of the circle but we know that the minion completes a revolution around a circle in 4 sec? 15. We can determine the angular velocity ω of the minion in rads/sec ω = 2 π rads T ω = 2 π rads 4 sec = 1.57 rads/sec 16. How far around the circle in rads would the minion move in 2.5 seconds? θ= ωt where θ = angular displacement in rads (θ is theta) θ = 1.57 rads/sec) (2.5 sec) =? = 3.9 rads 17. How many degrees is this? (3.9 rads) (57.3 /rad) =? 223 (a bit more than halfway)

17 18. A turn table completes one revolution in 5 seconds. If coin A is 4 meters from the center and coin B is 8 meters from the center, find the velocity of each coin. Velocity of coin A Velocity of coin B 19..Conclusion? V = 2 π r T V = 2 π r T V = 2 π 4m 5 s V = 2 π 8m 5 s = 5.0 m/s = 10.0 m/s The farther away an object is from the center of a circle the greater the velocity of that object Why? as the radius is increased - greater r in equation = greater V

18 After 5 seconds the turn table completes one revolution. 20. Each coin moves a total of 360 or 2 π rads while moving around the circle. So each coin moves the same angular distance in 5 seconds. That angular distance is 6.28 rads. If both coins move the same angular distance in the same time, they must have the same angular velocity (ω) measured in rads/sec. 21. ω = _θ_ = 6.28 rads t 5 sec = 1.25 rads/sec

19 A turn table completes one revolution in 5 seconds. If coin A is 4 meters from the center and coin B is 8 meters from the center, find the velocity of each coin. V of coin A = 5.0 m/s and r = 4 m V of coin B = 10.0 m/s and r = 8 m 22. Even though both coins have a different velocity in meters/sec they have the same angular velocity in rads/sec 23. v =ωr 24. Coin A v =ωr v = (1.25 rads/sec) (4 m) = 5 m/s 24. Coin B v =ωr v = (1.25 rads/sec) (8 m) = 10 m/s

20 25. All points on a rotating object rotate through the same angle in the same time 26. All points on a rotating object have the same angular velocity, ω, but different speeds, v, v =ωr.

21 Angular displacement = θ θ= ω t Angular Velocity = ω (Greek: Omega) ω = θ/t All points on a rotating object rotate through the same angle in the same time, and have the same frequency. Angular velocity: all points on a rotating object have the same angular velocity, ω, but different speeds, v, and v =ωr. v =ωr

22

23 Angular & Linear Velocity In symbols: v = r ω v r ω

24 How would you describe the velocity in this situation where an object is moving in a circle? Constantly changing! We say the velocity vector is Tangent to the circular path of travel and call it the Tangential velocity.

25 What happens when an object is spun on a string and the string breaks?

26 The object moves off in a straight line tangent to the circle

27 As an object moves around a circle, its direction of motion is constantly changing. Therefore its velocity is changing. Therefore an object moving in a circle is constantly accelerating. Acceleration

28 Centripetal Acceleration The acceleration of an object moving in a circle points toward the center of the circle. This is called a centripetal (center pointing) acceleration. a

29 Centripetal Acceleration The centripetal acceleration depends on: The speed of the object. The radius of the circle. a cent = v 2 r

30 Centripetal Force Newton s Second Law says that if an object is accelerating, there must be a net force on it. For an object moving in a circle, this is called the centripetal force. The centripetal force points toward the center of the circle.

31 Centripetal Force Centripetal force on an object depends on: The object s mass - more mass means more force. The object s speed - more speed means more force. And

32 Centripetal Force The centripetal force on an object also depends on: The object s distance from the axis (radius). If linear velocity is held constant, more distance requires less force. If angular velocity is held constant, more distance requires more force.

33 Centripetal Force In symbols: F cent = mv2 r

34 Centrifugal Force Centrifugal force is a fictitious force - it is not an interaction between 2 objects, and therefore not a real force. Nothing pulls an object away from the center of the circle.

35 Centrifugal Force What is erroneously attributed to centrifugal force is actually the action of the object s inertia - whatever velocity it has (speed + direction) it wants to keep.

When the ball reaches the break in the circle, which path will it follow?

When the ball reaches the break in the circle, which path will it follow? Checking Understanding: Circular Motion Dynamics When the ball reaches the break in the circle, which path will it follow? Slide 6-21 Answer When the ball reaches the break in the circle, which path will

More information

Chapter 8- Rotational Motion

Chapter 8- Rotational Motion Chapter 8- Rotational Motion Assignment 8 Textbook (Giancoli, 6 th edition), Chapter 7-8: Due on Thursday, November 13, 2008 - Problem 28 - page 189 of the textbook - Problem 40 - page 190 of the textbook

More information

Contents. Objectives Circular Motion Velocity and Acceleration Examples Accelerating Frames Polar Coordinates Recap. Contents

Contents. Objectives Circular Motion Velocity and Acceleration Examples Accelerating Frames Polar Coordinates Recap. Contents Physics 121 for Majors Today s Class You will see how motion in a circle is mathematically similar to motion in a straight line. You will learn that there is a centripetal acceleration (and force) and

More information

7.1 Describing Circular and Rotational Motion.notebook November 03, 2017

7.1 Describing Circular and Rotational Motion.notebook November 03, 2017 Describing Circular and Rotational Motion Rotational motion is the motion of objects that spin about an axis. Section 7.1 Describing Circular and Rotational Motion We use the angle θ from the positive

More information

Chapter 8 Lecture Notes

Chapter 8 Lecture Notes Chapter 8 Lecture Notes Physics 2414 - Strauss Formulas: v = l / t = r θ / t = rω a T = v / t = r ω / t =rα a C = v 2 /r = ω 2 r ω = ω 0 + αt θ = ω 0 t +(1/2)αt 2 θ = (1/2)(ω 0 +ω)t ω 2 = ω 0 2 +2αθ τ

More information

Periodic Motion. Circular Motion, Gravity, Simple Harmonic Motion

Periodic Motion. Circular Motion, Gravity, Simple Harmonic Motion Periodic Motion Circular Motion, Gravity, Simple Harmonic Motion Periodic Motion I. Circular Motion - kinematics & centripetal acceleration - dynamics & centripetal force - centrifugal force II. Universal

More information

Uniform Circular Motion AP

Uniform Circular Motion AP Uniform Circular Motion AP Uniform circular motion is motion in a circle at the same speed Speed is constant, velocity direction changes the speed of an object moving in a circle is given by v circumference

More information

1 Problems 1-3 A disc rotates about an axis through its center according to the relation θ (t) = t 4 /4 2t

1 Problems 1-3 A disc rotates about an axis through its center according to the relation θ (t) = t 4 /4 2t Slide 1 / 30 1 Problems 1-3 disc rotates about an axis through its center according to the relation θ (t) = t 4 /4 2t etermine the angular velocity of the disc at t= 2 s 2 rad/s 4 rad/s 6 rad/s 8 rad/s

More information

Slide 1 / 30. Slide 2 / 30. Slide 3 / m/s -1 m/s

Slide 1 / 30. Slide 2 / 30. Slide 3 / m/s -1 m/s 1 Problems 1-3 disc rotates about an axis through its center according to the relation θ (t) = t 4 /4 2t Slide 1 / 30 etermine the angular velocity of the disc at t= 2 s 2 rad/s 4 rad/s 6 rad/s 8 rad/s

More information

DEVIL PHYSICS BADDEST CLASS ON CAMPUS IB PHYSICS

DEVIL PHYSICS BADDEST CLASS ON CAMPUS IB PHYSICS DEVIL PHYSICS BADDEST CLASS ON CAMPUS IB PHYSICS OPTION B-1A: ROTATIONAL DYNAMICS Essential Idea: The basic laws of mechanics have an extension when equivalent principles are applied to rotation. Actual

More information

Uniform Circular Motion

Uniform Circular Motion Uniform Circular Motion Motion in a circle at constant angular speed. ω: angular velocity (rad/s) Rotation Angle The rotation angle is the ratio of arc length to radius of curvature. For a given angle,

More information

Circular Motion. Unit 7

Circular Motion. Unit 7 Circular Motion Unit 7 Do Now You drive a car that follows a circular path with the radius r = 100 m. Find the distance travelled if you made one complete circle. C 2 R 2(3.14)(100) 6.28(100) 628m Uniform

More information

Topic 6 The Killers LEARNING OBJECTIVES. Topic 6. Circular Motion and Gravitation

Topic 6 The Killers LEARNING OBJECTIVES. Topic 6. Circular Motion and Gravitation Topic 6 Circular Motion and Gravitation LEARNING OBJECTIVES Topic 6 The Killers 1. Centripetal Force 2. Newton s Law of Gravitation 3. Gravitational Field Strength ROOKIE MISTAKE! Always remember. the

More information

CIRCULAR MOTION AND ROTATION

CIRCULAR MOTION AND ROTATION 1. UNIFORM CIRCULAR MOTION So far we have learned a great deal about linear motion. This section addresses rotational motion. The simplest kind of rotational motion is an object moving in a perfect circle

More information

Kinematics. 1. Introduction to Kinematics. 2. Position and displacement

Kinematics. 1. Introduction to Kinematics. 2. Position and displacement Kinematics 1. Introduction to Kinematics. Scalars & vectors 2. Position & displacement 3. Velocity 4. Acceleration 5. Uniform linear motion 6. Uniformly accelerated motion 7. Uniform circular motion 1.

More information

Linear vs. Rotational Motion

Linear vs. Rotational Motion Linear vs. Rotational Motion Every term in a linear equation has a similar term in the analogous rotational equation. Displacements: s = r θ v t ω Speeds: v t = ω r Accelerations: a t = α r Every point

More information

Rotation Basics. I. Angular Position A. Background

Rotation Basics. I. Angular Position A. Background Rotation Basics I. Angular Position A. Background Consider a student who is riding on a merry-go-round. We can represent the student s location by using either Cartesian coordinates or by using cylindrical

More information

Complete the table by filling in the symbols and equations. Include any notes that will help you remember and understand what these terms mean.

Complete the table by filling in the symbols and equations. Include any notes that will help you remember and understand what these terms mean. AP Physics Rotational kinematics Rotational Kinematics Complete the table by filling in the symbols and equations. Include any notes that will help you remember and understand what these terms mean. Translational

More information

In physics, motion in circles is just as important as motion along lines, but there are all

In physics, motion in circles is just as important as motion along lines, but there are all Chapter 6 Round and Round: Circular Motion In This Chapter Converting angles Handling period and frequency Working with angular frequency Using angular acceleration In physics, motion in circles is just

More information

Circular Motion. Conceptual Physics 11 th Edition. Circular Motion Tangential Speed

Circular Motion. Conceptual Physics 11 th Edition. Circular Motion Tangential Speed Conceptual Physics 11 th Edition Circular Motion Rotational Inertia Torque Center of Mass and Center of Gravity Centripetal Force Centrifugal Force Chapter 8: ROTATION Rotating Reference Frames Simulated

More information

Lecture 3. Rotational motion and Oscillation 06 September 2018

Lecture 3. Rotational motion and Oscillation 06 September 2018 Lecture 3. Rotational motion and Oscillation 06 September 2018 Wannapong Triampo, Ph.D. Angular Position, Velocity and Acceleration: Life Science applications Recall last t ime. Rigid Body - An object

More information

UNIT 15 ROTATION KINEMATICS. Objectives

UNIT 15 ROTATION KINEMATICS. Objectives UNIT 5 ROTATION KINEMATICS Objectives to understand the concept of angular speed to understand the concept of angular acceleration to understand and be able to use kinematics equations to describe the

More information

7 Rotational Motion Pearson Education, Inc. Slide 7-2

7 Rotational Motion Pearson Education, Inc. Slide 7-2 7 Rotational Motion Slide 7-2 Slide 7-3 Recall from Chapter 6 Angular displacement = θ θ= ω t Angular Velocity = ω (Greek: Omega) ω = 2 π f and ω = θ/ t All points on a rotating object rotate through the

More information

Physics A - PHY 2048C

Physics A - PHY 2048C Physics A - PHY 2048C Newton s Laws & Equations of 09/27/2017 My Office Hours: Thursday 2:00-3:00 PM 212 Keen Building Warm-up Questions 1 In uniform circular motion (constant speed), what is the direction

More information

Rotational kinematics

Rotational kinematics Rotational kinematics Suppose you cut a circle out of a piece of paper and then several pieces of string which are just as long as the radius of the paper circle. If you then begin to lay these pieces

More information

Projectile Motion. directions simultaneously. deal with is called projectile motion. ! An object may move in both the x and y

Projectile Motion. directions simultaneously. deal with is called projectile motion. ! An object may move in both the x and y Projectile Motion! An object may move in both the x and y directions simultaneously! The form of two-dimensional motion we will deal with is called projectile motion Assumptions of Projectile Motion! The

More information

Chapter 8 Lecture. Pearson Physics. Rotational Motion and Equilibrium. Prepared by Chris Chiaverina Pearson Education, Inc.

Chapter 8 Lecture. Pearson Physics. Rotational Motion and Equilibrium. Prepared by Chris Chiaverina Pearson Education, Inc. Chapter 8 Lecture Pearson Physics Rotational Motion and Equilibrium Prepared by Chris Chiaverina Chapter Contents Describing Angular Motion Rolling Motion and the Moment of Inertia Torque Static Equilibrium

More information

Chapter 10 Rotational Kinematics and Energy. Copyright 2010 Pearson Education, Inc.

Chapter 10 Rotational Kinematics and Energy. Copyright 2010 Pearson Education, Inc. Chapter 10 Rotational Kinematics and Energy Copyright 010 Pearson Education, Inc. 10-1 Angular Position, Velocity, and Acceleration Copyright 010 Pearson Education, Inc. 10-1 Angular Position, Velocity,

More information

Chapter 8: Dynamics in a plane

Chapter 8: Dynamics in a plane 8.1 Dynamics in 2 Dimensions p. 210-212 Chapter 8: Dynamics in a plane 8.2 Velocity and Acceleration in uniform circular motion (a review of sec. 4.6) p. 212-214 8.3 Dynamics of Uniform Circular Motion

More information

UNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics

UNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics UNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics Physics 111.6 MIDTERM TEST #2 November 15, 2001 Time: 90 minutes NAME: STUDENT NO.: (Last) Please Print (Given) LECTURE SECTION

More information

PHYSICS 220 LAB #6: CIRCULAR MOTION

PHYSICS 220 LAB #6: CIRCULAR MOTION Name: Partners: PHYSICS 220 LAB #6: CIRCULAR MOTION The picture above is a copy of Copernicus drawing of the orbits of the planets which are nearly circular. It appeared in a book published in 1543. Since

More information

Chapter 7: Circular Motion

Chapter 7: Circular Motion Chapter 7: Circular Motion Spin about an axis located within the body Example: Spin about an axis located outside the body. Example: Example: Explain why it feels like you are pulled to the right side

More information

Rotational Kinematics, Physics. Worksheet 1: Practice working with rotation and revolution

Rotational Kinematics, Physics. Worksheet 1: Practice working with rotation and revolution Rotational Kinematics, Physics Worksheet 1: Practice working with rotation and revolution Circular motion can involve rotation and/or revolution. Rotation occurs when the object spins about an internal

More information

Phys101 Lectures 19, 20 Rotational Motion

Phys101 Lectures 19, 20 Rotational Motion Phys101 Lectures 19, 20 Rotational Motion Key points: Angular and Linear Quantities Rotational Dynamics; Torque and Moment of Inertia Rotational Kinetic Energy Ref: 10-1,2,3,4,5,6,8,9. Page 1 Angular Quantities

More information

Centripetal force keeps an Rotation and Revolution

Centripetal force keeps an Rotation and Revolution Centripetal force keeps an object in circular motion. Which moves faster on a merry-go-round, a horse near the outside rail or one near the inside rail? While a hamster rotates its cage about an axis,

More information

Physics 101 Discussion Week 12 Explanation (2011)

Physics 101 Discussion Week 12 Explanation (2011) Physics 101 Discussion Week 12 Eplanation (2011) D12-1 Horizontal oscillation Q0. This is obviously about a harmonic oscillator. Can you write down Newton s second law in the (horizontal) direction? Let

More information

Blueberry Muffin Nov. 29/30, 2016 Period: Names:

Blueberry Muffin Nov. 29/30, 2016 Period: Names: Blueberry Muffin Nov. 9/30, 016 Period: Names: Congratulations! 1. To solve the problems, use your etextbook, physical textbooks, physics websites, your Sketchbooks.. Show your thinking through calculations,

More information

Holt Physics Chapter 7. Rotational Motion

Holt Physics Chapter 7. Rotational Motion Holt Physics Chapter 7 Rotational Motion Measuring Rotational Motion Spinning objects have rotational motion Axis of rotation is the line about which rotation occurs A point that moves around an axis undergoes

More information

Physics 101: Lecture 08 Centripetal Acceleration and Circular Motion

Physics 101: Lecture 08 Centripetal Acceleration and Circular Motion Physics 101: Lecture 08 Centripetal Acceleration and Circular Motion http://www.youtube.com/watch?v=zyf5wsmxrai Today s lecture will cover Chapter 5 Physics 101: Lecture 8, Pg 1 Circular Motion Act B A

More information

Exam I Physics 101: Lecture 08 Centripetal Acceleration and Circular Motion Today s lecture will cover Chapter 5 Exam I is Monday, Oct. 7 (2 weeks!

Exam I Physics 101: Lecture 08 Centripetal Acceleration and Circular Motion Today s lecture will cover Chapter 5 Exam I is Monday, Oct. 7 (2 weeks! Exam I Physics 101: Lecture 08 Centripetal Acceleration and Circular Motion http://www.youtube.com/watch?v=zyf5wsmxrai Today s lecture will cover Chapter 5 Exam I is Monday, Oct. 7 ( weeks!) Physics 101:

More information

Physics. Chapter 8 Rotational Motion

Physics. Chapter 8 Rotational Motion Physics Chapter 8 Rotational Motion Circular Motion Tangential Speed The linear speed of something moving along a circular path. Symbol is the usual v and units are m/s Rotational Speed Number of revolutions

More information

CIRCULAR MOTION, HARMONIC MOTION, ROTATIONAL MOTION

CIRCULAR MOTION, HARMONIC MOTION, ROTATIONAL MOTION CIRCULAR MOTION, HARMONIC MOTION, ROTATIONAL MOTION 1 UNIFORM CIRCULAR MOTION path circle distance arc Definition: An object which moves on a circle, travels equal arcs in equal times. Periodic motion

More information

APC PHYSICS CHAPTER 11 Mr. Holl Rotation

APC PHYSICS CHAPTER 11 Mr. Holl Rotation APC PHYSICS CHAPTER 11 Mr. Holl Rotation Student Notes 11-1 Translation and Rotation All of the motion we have studied to this point was linear or translational. Rotational motion is the study of spinning

More information

1. Which of the following is the unit for angular displacement? A. Meters B. Seconds C. Radians D. Radian per second E. Inches

1. Which of the following is the unit for angular displacement? A. Meters B. Seconds C. Radians D. Radian per second E. Inches AP Physics B Practice Questions: Rotational Motion Multiple-Choice Questions 1. Which of the following is the unit for angular displacement? A. Meters B. Seconds C. Radians D. Radian per second E. Inches

More information

Rotation. PHYS 101 Previous Exam Problems CHAPTER

Rotation. PHYS 101 Previous Exam Problems CHAPTER PHYS 101 Previous Exam Problems CHAPTER 10 Rotation Rotational kinematics Rotational inertia (moment of inertia) Kinetic energy Torque Newton s 2 nd law Work, power & energy conservation 1. Assume that

More information

2. Relative and Circular Motion

2. Relative and Circular Motion 2. Relative and Circular Motion A) Overview We will begin with a discussion of relative motion in one dimension. We will describe this motion in terms of displacement and velocity vectors which will allow

More information

Rotational Motion and the Law of Gravity 1

Rotational Motion and the Law of Gravity 1 Rotational Motion and the Law of Gravity 1 Linear motion is described by position, velocity, and acceleration. Circular motion repeats itself in circles around the axis of rotation Ex. Planets in orbit,

More information

AP Physics 1 Lesson 15.a Rotational Kinematics Graphical Analysis and Kinematic Equation Use. Name. Date. Period. Engage

AP Physics 1 Lesson 15.a Rotational Kinematics Graphical Analysis and Kinematic Equation Use. Name. Date. Period. Engage AP Physics 1 Lesson 15.a Rotational Kinematics Graphical Analysis and Kinematic Equation Use Name Outcomes Date Interpret graphical evidence of angular motion (uniform speed & uniform acceleration). Apply

More information

Chapter 8: Rotational Motion

Chapter 8: Rotational Motion Lecture Outline Chapter 8: Rotational Motion This lecture will help you understand: Circular Motion Rotational Inertia Torque Center of Mass and Center of Gravity Centripetal Force Centrifugal Force Rotating

More information

Rigid Object. Chapter 10. Angular Position. Angular Position. A rigid object is one that is nondeformable

Rigid Object. Chapter 10. Angular Position. Angular Position. A rigid object is one that is nondeformable Rigid Object Chapter 10 Rotation of a Rigid Object about a Fixed Axis A rigid object is one that is nondeformable The relative locations of all particles making up the object remain constant All real objects

More information

Circular Motion Tangential Speed. Conceptual Physics 11 th Edition. Circular Motion Rotational Speed. Circular Motion

Circular Motion Tangential Speed. Conceptual Physics 11 th Edition. Circular Motion Rotational Speed. Circular Motion Conceptual Physics 11 th Edition Circular Motion Tangential Speed The distance traveled by a point on the rotating object divided by the time taken to travel that distance is called its tangential speed

More information

Fundamentals of Mathematics (MATH 1510)

Fundamentals of Mathematics (MATH 1510) Fundamentals of Mathematics () Instructor: Email: shenlili@yorku.ca Department of Mathematics and Statistics York University March 14-18, 2016 Outline 1 2 s An angle AOB consists of two rays R 1 and R

More information

What path do the longest sparks take after they leave the wand? Today we ll be doing one more new concept before the test on Wednesday.

What path do the longest sparks take after they leave the wand? Today we ll be doing one more new concept before the test on Wednesday. What path do the longest sparks take after they leave the wand? Today we ll be doing one more new concept before the test on Wednesday. Centripetal Acceleration and Newtonian Gravitation Reminders: 15

More information

Circular Motion & Rotational Mechanics. Semester 2 Review Project - Sonya Kalara, Ellie Kim, and Charlotte Spry

Circular Motion & Rotational Mechanics. Semester 2 Review Project - Sonya Kalara, Ellie Kim, and Charlotte Spry Circular Motion & Rotational Mechanics Semester 2 Review Project - Sonya Kalara, Ellie Kim, and Charlotte Spry Definitions II. III. IV. I. Uniform Circular Motion - an object that moves in a circle at

More information

第 1 頁, 共 7 頁 Chap10 1. Test Bank, Question 3 One revolution per minute is about: 0.0524 rad/s 0.105 rad/s 0.95 rad/s 1.57 rad/s 6.28 rad/s 2. *Chapter 10, Problem 8 The angular acceleration of a wheel

More information

Centripetal Force Exploring Uniform Circular Motion

Centripetal Force Exploring Uniform Circular Motion 1 Exploring Uniform Circular Motion An object that moves in a circle at constant speed, v, is said to experience uniform circular motion (UCM). The magnitude of the velocity remains constant, but the direction

More information

PHYS-2010: General Physics I Course Lecture Notes Section VIII

PHYS-2010: General Physics I Course Lecture Notes Section VIII PHYS-2010: General Physics I Course Lecture Notes Section VIII Dr. Donald G. Luttermoser East Tennessee State University Edition 2.4 Abstract These class notes are designed for use of the instructor and

More information

Circular Motion, Pt 2: Angular Dynamics. Mr. Velazquez AP/Honors Physics

Circular Motion, Pt 2: Angular Dynamics. Mr. Velazquez AP/Honors Physics Circular Motion, Pt 2: Angular Dynamics Mr. Velazquez AP/Honors Physics Formulas: Angular Kinematics (θ must be in radians): s = rθ Arc Length 360 = 2π rads = 1 rev ω = θ t = v t r Angular Velocity α av

More information

Exams will be returned on Tuesday. Apologies for the delay.

Exams will be returned on Tuesday. Apologies for the delay. Thursday February 21 Topics for this Lecture: Circular Motion Angular frequency Centripetal force/acceleration Fictitious (a.k.a. Inertial) forces: Centrifugal force Coriolis effect Gravity & orbits *Anything

More information

Rotation of Rigid Objects

Rotation of Rigid Objects Notes 12 Rotation and Extended Objects Page 1 Rotation of Rigid Objects Real objects have "extent". The mass is spread out over discrete or continuous positions. THERE IS A DISTRIBUTION OF MASS TO "AN

More information

Motion in Two Dimensions: Centripetal Acceleration

Motion in Two Dimensions: Centripetal Acceleration Motion in Two Dimensions: Centripetal Acceleration Name: Group Members: Date: TA s Name: Apparatus: Rotating platform, long string, liquid accelerometer, meter stick, masking tape, stopwatch Objectives:

More information

Circular motion, Center of Gravity, and Rotational Mechanics

Circular motion, Center of Gravity, and Rotational Mechanics Circular motion, Center of Gravity, and Rotational Mechanics Rotation and Revolution Every object moving in a circle turns around an axis. If the axis is internal to the object (inside) then it is called

More information

Section 9.2. Centripetal Acceleration Centripetal Force

Section 9.2. Centripetal Acceleration Centripetal Force Section 9.2 Centripetal Acceleration Centripetal Force Centripetal Acceleration Uniform Circular Motion The motion of an object in a circular path at a constant speed is known as uniform circular motion

More information

Circular Motion Ch. 10 in your text book

Circular Motion Ch. 10 in your text book Circular Motion Ch. 10 in your text book Objectives Students will be able to: 1) Define rotation and revolution 2) Calculate the rotational speed of an object 3) Calculate the centripetal acceleration

More information

Rotation. EMU Physics Department. Ali ÖVGÜN.

Rotation. EMU Physics Department. Ali ÖVGÜN. Rotation Ali ÖVGÜN EMU Physics Department www.aovgun.com Rotational Motion Angular Position and Radians Angular Velocity Angular Acceleration Rigid Object under Constant Angular Acceleration Angular and

More information

Chapter 7. Rotational Motion

Chapter 7. Rotational Motion Chapter 7 Rotational Motion In This Chapter: Angular Measure Angular Velocity Angular Acceleration Moment of Inertia Torque Rotational Energy and Work Angular Momentum Angular Measure In everyday life,

More information

Lecture PowerPoints. Chapter 10 Physics for Scientists and Engineers, with Modern Physics, 4 th edition Giancoli

Lecture PowerPoints. Chapter 10 Physics for Scientists and Engineers, with Modern Physics, 4 th edition Giancoli Lecture PowerPoints Chapter 10 Physics for Scientists and Engineers, with Modern Physics, 4 th edition Giancoli 2009 Pearson Education, Inc. This work is protected by United States copyright laws and is

More information

Circular motion minutes. 62 marks. theonlinephysicstutor.com. facebook.com/theonlinephysicstutor Page 1 of 22. Name: Class: Date: Time: Marks:

Circular motion minutes. 62 marks. theonlinephysicstutor.com. facebook.com/theonlinephysicstutor Page 1 of 22. Name: Class: Date: Time: Marks: Circular motion 2 Name: Class: Date: Time: 67 minutes Marks: 62 marks Comments: Page 1 of 22 1 A lead ball of mass 0.25 kg is swung round on the end of a string so that the ball moves in a horizontal circle

More information

Episode 225: Quantitative circular motion

Episode 225: Quantitative circular motion Episode 225: Quantitative circular motion Summary Discussion: Linear and angular velocity. (10 minutes) Worked example: Calculating ω. (10 minutes) Discussion: Degrees and radians. (5 minutes) Student

More information

Preparing for Six Flags Physics Concepts

Preparing for Six Flags Physics Concepts Preparing for Six Flags Physics Concepts uniform means constant, unchanging At a uniform speed, the distance traveled is given by Distance = speed x time At uniform velocity, the displacement is given

More information

Recap I. Angular position: Angular displacement: s. Angular velocity: Angular Acceleration:

Recap I. Angular position: Angular displacement: s. Angular velocity: Angular Acceleration: Recap I Angular position: Angular displacement: s Angular velocity: Angular Acceleration: Every point on a rotating rigid object has the same angular, but not the same linear motion! Recap II Circular

More information

Momentum Review. Lecture 13 Announcements. Multi-step problems: collision followed by something else. Center of Mass

Momentum Review. Lecture 13 Announcements. Multi-step problems: collision followed by something else. Center of Mass Lecture 13 Announcements 1. While you re waiting for class to start, please fill in the How to use the blueprint equation steps, in your own words.. Exam results: Momentum Review Equations p = mv Conservation

More information

Translational vs Rotational. m x. Connection Δ = = = = = = Δ = = = = = = Δ =Δ = = = = = 2 / 1/2. Work

Translational vs Rotational. m x. Connection Δ = = = = = = Δ = = = = = = Δ =Δ = = = = = 2 / 1/2. Work Translational vs Rotational / / 1/ Δ m x v dx dt a dv dt F ma p mv KE mv Work Fd / / 1/ θ ω θ α ω τ α ω ω τθ Δ I d dt d dt I L I KE I Work / θ ω α τ Δ Δ c t s r v r a v r a r Fr L pr Connection Translational

More information

Uniform Circular Motion

Uniform Circular Motion Slide 1 / 112 Uniform Circular Motion 2009 by Goodman & Zavorotniy Slide 2 / 112 Topics of Uniform Circular Motion (UCM) Kinematics of UCM Click on the topic to go to that section Period, Frequency, and

More information

Concepts in Physics. Wednesday, September 23

Concepts in Physics. Wednesday, September 23 1206 - Concepts in Physics Wednesday, September 23 NOTES Additional Tutorial available: THURSDAY 16:30 to 18:00 F536 this is for all first year physics students, so bring specific questions you have Tutorial

More information

Motion Part 4: Projectile Motion

Motion Part 4: Projectile Motion Motion Part 4: Projectile Motion Last modified: 28/03/2017 CONTENTS Projectile Motion Uniform Motion Equations Projectile Motion Equations Trajectory How to Approach Problems Example 1 Example 2 Example

More information

Rotation of Rigid Objects

Rotation of Rigid Objects Notes 12 Rotation and Extended Objects Page 1 Rotation of Rigid Objects Real objects have "extent". The mass is spread out over discrete or continuous positions. THERE IS A DISTRIBUTION OF MASS TO "AN

More information

Chapter 10.A. Rotation of Rigid Bodies

Chapter 10.A. Rotation of Rigid Bodies Chapter 10.A Rotation of Rigid Bodies P. Lam 7_23_2018 Learning Goals for Chapter 10.1 Understand the equations govern rotational kinematics, and know how to apply them. Understand the physical meanings

More information

Physics 101 Lab 6: Rotational Motion Dr. Timothy C. Black Fall, 2005

Physics 101 Lab 6: Rotational Motion Dr. Timothy C. Black Fall, 2005 Theoretical Discussion Physics 101 Lab 6: Rotational Motion Dr. Timothy C. Black Fall, 2005 An object moving in a circular orbit[1] at constant speed is said to be executing uniform circular motion. The

More information

A) Yes B) No C) Impossible to tell from the information given.

A) Yes B) No C) Impossible to tell from the information given. Does escape speed depend on launch angle? That is, if a projectile is given an initial speed v o, is it more likely to escape an airless, non-rotating planet, if fired straight up than if fired at an angle?

More information

We define angular displacement, θ, and angular velocity, ω. What's a radian?

We define angular displacement, θ, and angular velocity, ω. What's a radian? We define angular displacement, θ, and angular velocity, ω Units: θ = rad ω = rad/s What's a radian? Radian is the ratio between the length of an arc and its radius note: counterclockwise is + clockwise

More information

Chapter 8 Rotational Motion

Chapter 8 Rotational Motion Chapter 8 Rotational Motion Chapter 8 Rotational Motion In this chapter you will: Learn how to describe and measure rotational motion. Learn how torque changes rotational velocity. Explore factors that

More information

Uniform Circular Motion

Uniform Circular Motion Circular Motion Uniform Circular Motion Uniform Circular Motion Traveling with a constant speed in a circular path Even though the speed is constant, the acceleration is non-zero The acceleration responsible

More information

Things going in circles

Things going in circles Things going in circles Physics 211 Syracuse University, Physics 211 Spring 2019 Walter Freeman February 18, 2019 W. Freeman Things going in circles February 18, 2019 1 / 30 Announcements Homework 4 due

More information

where R represents the radius of the circle and T represents the period.

where R represents the radius of the circle and T represents the period. Chapter 3 Circular Motion Uniform circular motion is the motion of an object in a circle with a constant or uniform speed. Speed When moving in a circle, an object traverses a distance around the perimeter

More information

Chapter 8: Newton s Laws Applied to Circular Motion

Chapter 8: Newton s Laws Applied to Circular Motion Chapter 8: Newton s Laws Applied to Circular Motion Circular Motion Milky Way Galaxy Orbital Speed of Solar System: 220 km/s Orbital Period: 225 Million Years Mercury: 48 km/s Venus: 35 km/s Earth: 30

More information

MECHANICAL PRINCIPLES OUTCOME 3 CENTRIPETAL ACCELERATION AND CENTRIPETAL FORCE TUTORIAL 1 CENTRIFUGAL FORCE

MECHANICAL PRINCIPLES OUTCOME 3 CENTRIPETAL ACCELERATION AND CENTRIPETAL FORCE TUTORIAL 1 CENTRIFUGAL FORCE MECHANICAL PRINCIPLES OUTCOME 3 CENTRIPETAL ACCELERATION AND CENTRIPETAL FORCE TUTORIAL 1 CENTRIFUGAL FORCE Centripetal acceleration and force: derivation of expressions for centripetal acceleration and

More information

Chapter 6: Systems in Motion

Chapter 6: Systems in Motion Chapter 6: Systems in Motion The celestial order and the beauty of the universe compel me to admit that there is some excellent and eternal Being, who deserves the respect and homage of men Cicero (106

More information

Chapter 9 [ Edit ] Ladybugs on a Rotating Disk. v = ωr, where r is the distance between the object and the axis of rotation. Chapter 9. Part A.

Chapter 9 [ Edit ] Ladybugs on a Rotating Disk. v = ωr, where r is the distance between the object and the axis of rotation. Chapter 9. Part A. Chapter 9 [ Edit ] Chapter 9 Overview Summary View Diagnostics View Print View with Answers Due: 11:59pm on Sunday, October 30, 2016 To understand how points are awarded, read the Grading Policy for this

More information

6. Find the net torque on the wheel in Figure about the axle through O if a = 10.0 cm and b = 25.0 cm.

6. Find the net torque on the wheel in Figure about the axle through O if a = 10.0 cm and b = 25.0 cm. 1. During a certain period of time, the angular position of a swinging door is described by θ = 5.00 + 10.0t + 2.00t 2, where θ is in radians and t is in seconds. Determine the angular position, angular

More information

Game Physics. Game and Media Technology Master Program - Utrecht University. Dr. Nicolas Pronost

Game Physics. Game and Media Technology Master Program - Utrecht University. Dr. Nicolas Pronost Game and Media Technology Master Program - Utrecht University Dr. Nicolas Pronost Essential physics for game developers Introduction The primary issues Let s move virtual objects Kinematics: description

More information

Centripetal Acceleration & Angular Momentum. Physics - 4 th Six Weeks

Centripetal Acceleration & Angular Momentum. Physics - 4 th Six Weeks Centripetal Acceleration & Angular Momentum Physics - 4 th Six Weeks Centripetal Force and Acceleration Centripetal Acceleration (A C ) is the acceleration of an object towards the center of a curved or

More information

Worksheet for Exploration 10.1: Constant Angular Velocity Equation

Worksheet for Exploration 10.1: Constant Angular Velocity Equation Worksheet for Exploration 10.1: Constant Angular Velocity Equation By now you have seen the equation: θ = θ 0 + ω 0 *t. Perhaps you have even derived it for yourself. But what does it really mean for the

More information

Chapter 5 Lecture Notes

Chapter 5 Lecture Notes Formulas: a C = v 2 /r a = a C + a T F = Gm 1 m 2 /r 2 Chapter 5 Lecture Notes Physics 2414 - Strauss Constants: G = 6.67 10-11 N-m 2 /kg 2. Main Ideas: 1. Uniform circular motion 2. Nonuniform circular

More information

Centripetal acceleration

Centripetal acceleration Book page 250-252 cgrahamphysics.com 2016 Centripetal acceleration Acceleration for circular motion Linear acceleration a = v = v u t t For circular motion: Instantaneous velocity is always tangent to

More information

Angle recap. Angular position: Angular displacement: s. Angular velocity: Angular Acceleration:

Angle recap. Angular position: Angular displacement: s. Angular velocity: Angular Acceleration: Angle recap Angular position: Angular displacement: s Angular velocity: Angular Acceleration: Every point on a rotating rigid object has the same angular, but not the same linear motion! Today s lecture

More information

Chapter 7. Rotational Motion and The Law of Gravity

Chapter 7. Rotational Motion and The Law of Gravity Chapter 7 Rotational Motion and The Law of Gravity 1 The Radian The radian is a unit of angular measure The radian can be defined as the arc length s along a circle divided by the radius r s θ = r 2 More

More information

= o + t = ot + ½ t 2 = o + 2

= o + t = ot + ½ t 2 = o + 2 Chapters 8-9 Rotational Kinematics and Dynamics Rotational motion Rotational motion refers to the motion of an object or system that spins about an axis. The axis of rotation is the line about which the

More information

There are two ways of defining acceleration we need to be aware of.

There are two ways of defining acceleration we need to be aware of. www.liontutors.com PHYS 250 Exam 1 Supplement Circular Motion Centripetal Acceleration There are two ways of defining acceleration we need to be aware of. The one we ve been using so far deals with linear

More information

Test, Lesson 7 Waves - Answer Key Page 1

Test, Lesson 7 Waves - Answer Key Page 1 Test, Lesson 7 Waves - Answer Key Page 1 1. Match the proper units with the following: W. wavelength 1. nm F. frequency 2. /sec V. velocity 3. m 4. ms -1 5. Hz 6. m/sec (A) W: 1, 3 F: 2, 4, 5 V: 6 (B)

More information