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

Size: px
Start display at page:

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

Transcription

1 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

2 ROOKIE MISTAKE! Always remember. the formulae for centripetal force and gravitational fore are equal when considering orbits. 1 Centripetal Force Radians Measuring angles in degrees becomes less useful in advanced maths and physics, because they are arbitrary. Radians are used because they are multiples of π, which is a natural number and the natural unit for trigonometric functions. The angle in radians, θ, is defined as the arc-length divided by the radius.

3 Radians For a complete circle: θ = arc-length = 2πr = 2π rads radius r Any other angles are a fraction of 2π Degrees and Radians Degrees π/2 Radians π π π/4 Angular Displacement, θ Angular displacement, θ, is the angle in radians (or degrees) through which a point has been rotated about a specified axis. Angular Displacement, θ

4 Linear Velocity Linear velocity (or tangential velocity) is the velocity of a point on a rotating object. It is given by the equation: v = 2πr t Where r is the radius of the point and t is the time taken for one revolution. Units of v are ms -1 Linear Velocity Consider a rotating bicycle wheel: The radius is smaller for the red point, but the time taken for one complete revolution remains the same. vred < vblue Angular Velocity Angular velocity is the rate of change of angular displacement with respect to time It is given by the equation: ω = θ t Where θ is the angular displacement and t is the time taken. Units of ω are rads -1

5 Angular Velocity Consider the rotating bicycle wheel again: As the wheel rotates, the angle subtended by both red and blue points is the same, with respect to time. ωred = ωblue Linear and Angular Velocity The relationship linking linear (tangential) and angular velocity is: v=ωr Velocity Changes When an object travels at a constant speed in circular motion, the velocity is constantly changing due to the constant change in direction. If velocity is changing then the object is accelerating

6 Centripetal Acceleration Acceleration is defined as the rate of change of velocity. Consider the change of direction of velocity below: When an object is in circular motion, the acceleration of the object is always directed towards the centre of the circle. ACTUAL EXAMINER FEEDBACK Candidates were unable to use a vector diagram to explain the need for a centripetal force in circular motion. Acceleration Expressions Centripetal Acceleration a = v r 2 Angular Acceleration a = ω 2 r measured in ms -2 measured in rads -2

7 Centripetal Force Newton s 2nd Law states: Resultant force equals mass times acceleration in the direction if the force. An object in circular motion always experiences a force directed towards the centre of the circle. Force Expressions Using Centripetal Acceleration F = ma = mv 2 r Using Angular Acceleration F = ma = mω 2 r Measured in Newtons, N Topic 6 The Killers 1. Centripetal Force 2. Newton s Law of Gravitation

8 Gravitational Force Gravitational force acts at a distance and has an associated force field Newtons 3rd Law: Earth exerts a gravitational force on the Moon. Moon exerts an equal and opposite gravitational force on the Earth. Gravity is the weakest force and is only measurable with large masses (e.g. planet sizes) Gravitational Force The size of the gravitational force is: Newton s Law of Gravitation, where: ACTUAL EXAMINER FEEDBACK Candidates could not provide a statement to encompass Newton s Law of Gravitation

9 Gravitational Force The size of the gravitational force is: Directly proportional to the product of the masses Indirectly proportional to the square of the distance between the masses Assumption: masses have uniform density and the mass is concentrated at the centre (i.e. point masses) Orbits The size of the gravitational force is EQUAL TO the centripetal force Kepler s Law Not directly examined BUT Recent paper has asked to prove: WHAT?!?

10 Kepler s Law Not directly examined BUT Recent paper has asked to prove: Start Here: Substitute into above: rearrange and. Topic 6 The Killers 1. Centripetal Force 2. Newton s Law of Gravitation 3. Gravitational Field Strength Gravitational Field Strength A test mass is needed to define the strength of the gravitational field surrounding a large mass The test mass must have negligible gravitational effect i.e. very small mass Gravitational field strength is the force per unit mass experienced by a small test mass:

11 Gravitational Field Strength Gravitational field strength is the force per unit mass experienced by a small test mass: Gravitational Field Lines Gravitational field strength is a vector Gravity is always attractive Find lines point towards the centre of the massive object Field lines are perpendicular to the surface Lines are closer together near the surface - g is greater near the surface. Line are further apart as distance increases from the surface - g decreases with distance. Special Relationship Outside the spherical mass: g is inversely proportional to the r 2 (distance from centre of mass) Inside the spherical mass: g is directly proportional to r from the centre of the mass (assuming uniform density).

12 Two Bodies The syllabus says the students should be able to determine the resultant gravitational field strength due to two bodies along a straight line. Question 3m 3m 6m Calculate the resultant gravitational field at P.

Chapter 5 Centripetal Force and Gravity. Copyright 2010 Pearson Education, Inc.

Chapter 5 Centripetal Force and Gravity. Copyright 2010 Pearson Education, Inc. Chapter 5 Centripetal Force and Gravity v Centripetal Acceleration v Velocity is a Vector v It has Magnitude and Direction v If either changes, the velocity vector changes. Tumble Buggy Demo v Centripetal

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

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

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

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

Uniform circular motion (UCM) is the motion of an object in a perfect circle with a constant or uniform speed. Uniform circular motion (UCM) is the motion of an object in a perfect circle with a constant or uniform speed. 1. Distance around a circle? circumference 2. Distance from one side of circle to the opposite

More information

Circular Motion. Gravitation

Circular Motion. Gravitation Circular Motion Gravitation Circular Motion Uniform circular motion is motion in a circle at constant speed. Centripetal force is the force that keeps an object moving in a circle. Centripetal acceleration,

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

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

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

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

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

AP Physics 1 Chapter 7 Circular Motion and Gravitation

AP Physics 1 Chapter 7 Circular Motion and Gravitation AP Physics 1 Chapter 7 Circular Motion and Gravitation Chapter 7: Circular Motion and Angular Measure Gravitation Angular Speed and Velocity Uniform Circular Motion and Centripetal Acceleration Angular

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

Newton s Gravitational Law

Newton s Gravitational Law 1 Newton s Gravitational Law Gravity exists because bodies have masses. Newton s Gravitational Law states that the force of attraction between two point masses is directly proportional to the product of

More information

Key Points: Learn the relationship between gravitational attractive force, mass and distance. Understand that gravity can act as a centripetal force.

Key Points: Learn the relationship between gravitational attractive force, mass and distance. Understand that gravity can act as a centripetal force. Lesson 9: Universal Gravitation and Circular Motion Key Points: Learn the relationship between gravitational attractive force, mass and distance. Understand that gravity can act as a centripetal force.

More information

Topic 6 Circular Motion and Gravitation

Topic 6 Circular Motion and Gravitation Topic 6 Circular Motion and Gravitation Exam-Style Questions 1 a) Calculate the angular velocity of a person standing on the Earth s surface at sea level. b) The summit of Mount Everest is 8848m above

More information

Rotational Motion Examples:

Rotational Motion Examples: Rotational Motion Examples: 1. A 60. cm diameter wheel rotates through 50. rad. a. What distance will it move? b. How many times will the wheel rotate in this time? 2. A saw blade is spinning at 2000.

More information

Chapter 13: universal gravitation

Chapter 13: universal gravitation Chapter 13: universal gravitation Newton s Law of Gravitation Weight Gravitational Potential Energy The Motion of Satellites Kepler s Laws and the Motion of Planets Spherical Mass Distributions Apparent

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

Physics Test 7: Circular Motion page 1

Physics Test 7: Circular Motion page 1 Name Physics Test 7: Circular Motion page 1 hmultiple Choice Read each question and choose the best answer by putting the corresponding letter in the blank to the left. 1. The SI unit of angular speed

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

Circular Motion Test Review

Circular Motion Test Review Circular Motion Test Review Name: Date: 1) Is it possible for an object moving with a constant speed to accelerate? Explain. A) No, if the speed is constant then the acceleration is equal to zero. B) No,

More information

Slide 1 / 37. Rotational Motion

Slide 1 / 37. Rotational Motion Slide 1 / 37 Rotational Motion Slide 2 / 37 Angular Quantities An angle θ can be given by: where r is the radius and l is the arc length. This gives θ in radians. There are 360 in a circle or 2π radians.

More information

Radians & Radius. Circumference = 2πr Part s = θ r r. θ=s/r. θ in radians! 360 o =2π rad = 6.28 rad θ (rad) = π/180 o θ (deg)

Radians & Radius. Circumference = 2πr Part s = θ r r. θ=s/r. θ in radians! 360 o =2π rad = 6.28 rad θ (rad) = π/180 o θ (deg) Radians & Radius Circumference = 2πr Part s = θ r r s θ θ in radians! 360 o =2π rad = 6.28 rad θ (rad) = π/180 o θ (deg) θ=s/r 1 Angular speed and acceleration θ f ϖ = t ω = f lim Δt 0 θ t i i Δθ Δt =

More information

Lecture 1a: Satellite Orbits

Lecture 1a: Satellite Orbits Lecture 1a: Satellite Orbits Meteorological Satellite Orbits LEO view GEO view Two main orbits of Met Satellites: 1) Geostationary Orbit (GEO) 1) Low Earth Orbit (LEO) or polar orbits Orbits of meteorological

More information

Nm kg. The magnitude of a gravitational field is known as the gravitational field strength, g. This is defined as the GM

Nm kg. The magnitude of a gravitational field is known as the gravitational field strength, g. This is defined as the GM Copyright FIST EDUCATION 011 0430 860 810 Nick Zhang Lecture 7 Gravity and satellites Newton's Law of Universal Gravitation Gravitation is a force of attraction that acts between any two masses. The gravitation

More information

Acceleration in Uniform Circular Motion

Acceleration in Uniform Circular Motion Acceleration in Uniform Circular Motion The object in uniform circular motion has a constant speed, but its velocity is constantly changing directions, generating a centripetal acceleration: a c v r 2

More information

CIRCULAR MOTION AND UNIVERSAL GRAVITATION

CIRCULAR MOTION AND UNIVERSAL GRAVITATION CIRCULAR MOTION AND UNIVERSAL GRAVITATION Uniform Circular Motion What holds an object in a circular path? A force. String Friction Gravity What happens when the force is diminished? Object flies off in

More information

Lecture PowerPoints. Chapter 8 Physics: Principles with Applications, 6 th edition Giancoli

Lecture PowerPoints. Chapter 8 Physics: Principles with Applications, 6 th edition Giancoli Lecture PowerPoints Chapter 8 Physics: Principles with Applications, 6 th edition Giancoli 2005 Pearson Prentice Hall This work is protected by United States copyright laws and is provided solely for the

More information

Ron Ferril SBCC Physics 101 Chapter Jun07A Page 1 of 22. Chapter 03 Rotation, Gravity, Projectiles and Spacecraft

Ron Ferril SBCC Physics 101 Chapter Jun07A Page 1 of 22. Chapter 03 Rotation, Gravity, Projectiles and Spacecraft Ron Ferril SBCC Physics 101 Chapter 03 2017Jun07A Page 1 of 22 Chapter 03 Rotation, Gravity, Projectiles and Spacecraft Angular Quantities Previous chapters involved the linear quantities mass, displacement,

More information

Rotational Kinematics

Rotational Kinematics Rotational Kinematics Rotational Coordinates Ridged objects require six numbers to describe their position and orientation: 3 coordinates 3 axes of rotation Rotational Coordinates Use an angle θ to describe

More information

Cp physics web review chapter 7 gravitation and circular motion

Cp physics web review chapter 7 gravitation and circular motion Name: Class: _ Date: _ ID: A Cp physics web review chapter 7 gravitation and circular motion Multiple Choice Identify the choice that best completes the statement or answers the question.. What is the

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

Axis Balanced Forces Centripetal force. Change in velocity Circular Motion Circular orbit Collision. Conservation of Energy

Axis Balanced Forces Centripetal force. Change in velocity Circular Motion Circular orbit Collision. Conservation of Energy When something changes its velocity The rate of change of velocity of a moving object. Can result from a change in speed and/or a change in direction On surface of earth, value is 9.8 ms-²; increases nearer

More information

Lecture 13 REVIEW. Physics 106 Spring What should we know? What should we know? Newton s Laws

Lecture 13 REVIEW. Physics 106 Spring What should we know? What should we know? Newton s Laws Lecture 13 REVIEW Physics 106 Spring 2006 http://web.njit.edu/~sirenko/ What should we know? Vectors addition, subtraction, scalar and vector multiplication Trigonometric functions sinθ, cos θ, tan θ,

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

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

Gravitation and Newton s Synthesis

Gravitation and Newton s Synthesis Lecture 10 Chapter 6 Physics I 0.4.014 Gravitation and Newton s Synthesis Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsi Lecture Capture: http://echo360.uml.edu/danylov013/physics1spring.html

More information

Chapter 5 Review : Circular Motion; Gravitation

Chapter 5 Review : Circular Motion; Gravitation Chapter 5 Review : Circular Motion; Gravitation Conceptual Questions 1) Is it possible for an object moving with a constant speed to accelerate? Explain. A) No, if the speed is constant then the acceleration

More information

Exam Question 6/8 (HL/OL): Circular and Simple Harmonic Motion. February 1, Applied Mathematics: Lecture 7. Brendan Williamson.

Exam Question 6/8 (HL/OL): Circular and Simple Harmonic Motion. February 1, Applied Mathematics: Lecture 7. Brendan Williamson. in a : Exam Question 6/8 (HL/OL): Circular and February 1, 2017 in a This lecture pertains to material relevant to question 6 of the paper, and question 8 of the Ordinary Level paper, commonly referred

More information

Physics 1A. Lecture 10B

Physics 1A. Lecture 10B Physics 1A Lecture 10B Review of Last Lecture Rotational motion is independent of translational motion A free object rotates around its center of mass Objects can rotate around different axes Natural unit

More information

Physics 1100: Uniform Circular Motion & Gravity

Physics 1100: Uniform Circular Motion & Gravity Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Physics 1100: Uniform Circular Motion & Gravity 1. In the diagram below, an object travels over a hill, down a valley, and around a loop the loop at constant

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

Its SI unit is rad/s and is an axial vector having its direction given by right hand thumb rule.

Its SI unit is rad/s and is an axial vector having its direction given by right hand thumb rule. Circular motion An object is said to be having circular motion if it moves along a circular path. For example revolution of moon around earth, the revolution of an artificial satellite in circular orbit

More information

Experiencing Acceleration: The backward force you feel when your car accelerates is caused by your body's inertia. Chapter 3.3

Experiencing Acceleration: The backward force you feel when your car accelerates is caused by your body's inertia. Chapter 3.3 Experiencing Acceleration: The backward force you feel when your car accelerates is caused by your body's inertia. Chapter 3.3 Feeling of apparent weight: Caused your body's reaction to the push that the

More information

AP Physics 1 Multiple Choice Questions - Chapter 7

AP Physics 1 Multiple Choice Questions - Chapter 7 1 A grindstone increases in angular speed from 4.00 rad/sec to 12.00 rad/sec in 4.00 seconds. Through what angle does it turn during that time if the angular acceleration is constant? a 8.00 rad b 12.0

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

Explain how it is possible for the gravitational force to cause the satellite to accelerate while its speed remains constant.

Explain how it is possible for the gravitational force to cause the satellite to accelerate while its speed remains constant. YEAR 12 PHYSICS: GRAVITATION PAST EXAM QUESTIONS Name: QUESTION 1 (1995 EXAM) (a) State Newton s Universal Law of Gravitation in words (b) A satellite of mass (m) moves in orbit of a planet with mass (M).

More information

Gravitation and Newton s Synthesis

Gravitation and Newton s Synthesis Lecture 10 Chapter 6 Physics I 0.4.014 Gravitation and Newton s Synthesis Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsi Lecture Capture: http://echo360.uml.edu/danylov013/physics1spring.html

More information

Gravitation. Kepler s Law. BSc I SEM II (UNIT I)

Gravitation. Kepler s Law. BSc I SEM II (UNIT I) Gravitation Kepler s Law BSc I SEM II (UNIT I) P a g e 2 Contents 1) Newton s Law of Gravitation 3 Vector representation of Newton s Law of Gravitation 3 Characteristics of Newton s Law of Gravitation

More information

Universal Gravitation

Universal Gravitation Universal Gravitation Newton s Law of Universal Gravitation Every particle in the Universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely

More information

AP Physics QUIZ Gravitation

AP Physics QUIZ Gravitation AP Physics QUIZ Gravitation Name: 1. If F1 is the magnitude of the force exerted by the Earth on a satellite in orbit about the Earth and F2 is the magnitude of the force exerted by the satellite on the

More information

Section Study Guide. Teacher Notes and Answers. Circular Motion and Gravitation

Section Study Guide. Teacher Notes and Answers. Circular Motion and Gravitation Section Study Guide Teacher Notes and Answers CIRCULAR MOTION 1. a. yes b. The car has a non-zero acceleration because the direction of motion is changing. c. The direction of centripetal acceleration

More information

Chapter 9 Lecture. Pearson Physics. Gravity and Circular Motion. Prepared by Chris Chiaverina Pearson Education, Inc.

Chapter 9 Lecture. Pearson Physics. Gravity and Circular Motion. Prepared by Chris Chiaverina Pearson Education, Inc. Chapter 9 Lecture Pearson Physics Gravity and Circular Motion Prepared by Chris Chiaverina Chapter Contents Newton's Law of Universal Gravity Applications of Gravity Circular Motion Planetary Motion and

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

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

Question 1. GRAVITATION UNIT H.W. ANS KEY

Question 1. GRAVITATION UNIT H.W. ANS KEY Question 1. GRAVITATION UNIT H.W. ANS KEY Question 2. Question 3. Question 4. Two stars, each of mass M, form a binary system. The stars orbit about a point a distance R from the center of each star, as

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

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

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

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

AP Physics QUIZ Chapters 10

AP Physics QUIZ Chapters 10 Name: 1. Torque is the rotational analogue of (A) Kinetic Energy (B) Linear Momentum (C) Acceleration (D) Force (E) Mass A 5-kilogram sphere is connected to a 10-kilogram sphere by a rigid rod of negligible

More information

PHYSICS 12 NAME: Gravitation

PHYSICS 12 NAME: Gravitation NAME: Gravitation 1. The gravitational force of attraction between the Sun and an asteroid travelling in an orbit of radius 4.14x10 11 m is 4.62 x 10 17 N. What is the mass of the asteroid? 2. A certain

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

Chapter 3.5. Uniform Circular Motion

Chapter 3.5. Uniform Circular Motion Chapter 3.5 Uniform Circular Motion 3.5 Uniform Circular Motion DEFINITION OF UNIFORM CIRCULAR MOTION Uniform circular motion is the motion of an object traveling at a constant speed on a circular path.

More information

Circular Motion and Gravitation. Centripetal Acceleration

Circular Motion and Gravitation. Centripetal Acceleration Circular Motion and Gravitation Centripetal Acceleration Recall linear acceleration 3. Going around a curve, at constant speed 1. Speeding up vi vi Δv a ac ac vi ac 2. Slowing down v velocity and acceleration

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

150 Lecture Notes - Section 6.1 Angle Measure

150 Lecture Notes - Section 6.1 Angle Measure c Marcia Drost, February, 008 Definition of Terms 50 Lecture Notes - Section 6. Angle Measure ray a line angle vertex two rays with a common endpoint the common endpoint initial side terminal side Standard

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

HW Chapter 5 Q 7,8,18,21 P 4,6,8. Chapter 5. The Law of Universal Gravitation Gravity

HW Chapter 5 Q 7,8,18,21 P 4,6,8. Chapter 5. The Law of Universal Gravitation Gravity HW Chapter 5 Q 7,8,18,21 P 4,6,8 Chapter 5 The Law of Universal Gravitation Gravity Newton s Law of Universal Gravitation Every particle in the Universe attracts every other particle with a force that

More information

Why Doesn t the Moon Hit us? In analysis of this question, we ll look at the following things: i. How do we get the acceleration due to gravity out

Why Doesn t the Moon Hit us? In analysis of this question, we ll look at the following things: i. How do we get the acceleration due to gravity out Why Doesn t the oon Hit us? In analysis of this question, we ll look at the following things: i. How do we get the acceleration due to gravity out of the equation for the force of gravity? ii. How does

More information

Version 001 circular and gravitation holland (2383) 1

Version 001 circular and gravitation holland (2383) 1 Version 00 circular and gravitation holland (383) This print-out should have 9 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. AP B 993 MC

More information

Quantitative Skills in AP Physics 1

Quantitative Skills in AP Physics 1 This chapter focuses on some of the quantitative skills that are important in your AP Physics 1 course. These are not all of the skills that you will learn, practice, and apply during the year, but these

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

AP Physics Multiple Choice Practice Gravitation

AP Physics Multiple Choice Practice Gravitation AP Physics Multiple Choice Practice Gravitation 1. Each of five satellites makes a circular orbit about an object that is much more massive than any of the satellites. The mass and orbital radius of each

More information

A Level. A Level Physics. Circular Motion (Answers) Edexcel. Name: Total Marks: /30

A Level. A Level Physics. Circular Motion (Answers) Edexcel. Name: Total Marks: /30 Visit http://www.mathsmadeeasy.co.uk/ for more fantastic resources. Edexcel A Level A Level Physics Circular Motion (Answers) Name: Total Marks: /30 Maths Made Easy Complete Tuition Ltd 2017 1. Total for

More information

Basic Physics. Isaac Newton ( ) Topics. Newton s Laws of Motion (2) Newton s Laws of Motion (1) PHYS 1411 Introduction to Astronomy

Basic Physics. Isaac Newton ( ) Topics. Newton s Laws of Motion (2) Newton s Laws of Motion (1) PHYS 1411 Introduction to Astronomy PHYS 1411 Introduction to Astronomy Basic Physics Chapter 5 Topics Newton s Laws Mass and Weight Work, Energy and Conservation of Energy Rotation, Angular velocity and acceleration Centripetal Force Angular

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

= 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

Lecture 6. Circular Motion. Pre-reading: KJF 6.1 and 6.2. Please take a clicker CIRCULAR MOTION KJF

Lecture 6. Circular Motion. Pre-reading: KJF 6.1 and 6.2. Please take a clicker CIRCULAR MOTION KJF Lecture 6 Circular Motion Pre-reading: KJF 6.1 and 6.2 Please take a clicker CIRCULAR MOTION KJF 6.1 6.4 Angular position If an object moves in a circle of radius r, then after travelling a distance s

More information

Circular Motion & Gravitation MC Question Database

Circular Motion & Gravitation MC Question Database (Questions #4,5,6,27,37,38,42 and 58 each have TWO correct answers.) 1) A record player has four coins at different distances from the center of rotation. Coin A is 1 cm away, Coin B is 2 cm away. Coin

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

II. Universal Gravitation - Newton 4th Law

II. Universal Gravitation - Newton 4th Law Periodic Motion I. Circular Motion - kinematics & centripetal acceleration - dynamics & centripetal force - centrifugal force II. Universal Gravitation - Newton s 4 th Law - force fields & orbits III.

More information

Topic 1: Newtonian Mechanics Energy & Momentum

Topic 1: Newtonian Mechanics Energy & Momentum Work (W) the amount of energy transferred by a force acting through a distance. Scalar but can be positive or negative ΔE = W = F! d = Fdcosθ Units N m or Joules (J) Work, Energy & Power Power (P) the

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

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

Connection between angular and linear speed

Connection between angular and linear speed Connection between angular and linear speed If a point-like object is in motion on a circular path of radius R at an instantaneous speed v, then its instantaneous angular speed ω is v = ω R Example: A

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

Precalculus Lesson 6.1: Angles and Their Measure Lesson 6.2: A Unit Circle Approach Part 2

Precalculus Lesson 6.1: Angles and Their Measure Lesson 6.2: A Unit Circle Approach Part 2 Precalculus Lesson 6.1: Angles and Their Measure Lesson 6.2: A Unit Circle Approach Part 2 Lesson 6.2 Before we look at the unit circle with respect to the trigonometric functions, we need to get some

More information

Physics for Scientists and Engineers 4th Edition, 2017

Physics for Scientists and Engineers 4th Edition, 2017 A Correlation of Physics for Scientists and Engineers 4th Edition, 2017 To the AP Physics C: Mechanics Course Descriptions AP is a trademark registered and/or owned by the College Board, which was not

More information

CHAPTER 7 GRAVITATION

CHAPTER 7 GRAVITATION Physics Approximate Timeline Students are expected to keep up with class work when absent. CHAPTER 7 GRAVITATION Day Plans for the day Assignments for the day 1 7.1 Planetary Motion & Gravitation Assignment

More information

Rotational Motion About a Fixed Axis

Rotational Motion About a Fixed Axis Rotational Motion About a Fixed Axis Vocabulary rigid body axis of rotation radian average angular velocity instantaneous angular average angular Instantaneous angular frequency velocity acceleration acceleration

More information

Chapter 13. Gravitation

Chapter 13. Gravitation Chapter 13 Gravitation e = c/a A note about eccentricity For a circle c = 0 à e = 0 a Orbit Examples Mercury has the highest eccentricity of any planet (a) e Mercury = 0.21 Halley s comet has an orbit

More information

Questions Chapter 13 Gravitation

Questions Chapter 13 Gravitation Questions Chapter 13 Gravitation 13-1 Newton's Law of Gravitation 13-2 Gravitation and Principle of Superposition 13-3 Gravitation Near Earth's Surface 13-4 Gravitation Inside Earth 13-5 Gravitational

More information

Physics 2211 M Quiz #2 Solutions Summer 2017

Physics 2211 M Quiz #2 Solutions Summer 2017 Physics 2211 M Quiz #2 Solutions Summer 2017 I. (16 points) A block with mass m = 10.0 kg is on a plane inclined θ = 30.0 to the horizontal, as shown. A balloon is attached to the block to exert a constant

More information

Physics 12. Unit 5 Circular Motion and Gravitation Part 1

Physics 12. Unit 5 Circular Motion and Gravitation Part 1 Physics 12 Unit 5 Circular Motion and Gravitation Part 1 1. Nonlinear motions According to the Newton s first law, an object remains its tendency of motion as long as there is no external force acting

More information

Chapter 9 Uniform Circular Motion

Chapter 9 Uniform Circular Motion 9.1 Introduction Chapter 9 Uniform Circular Motion Special cases often dominate our study of physics, and circular motion is certainly no exception. We see circular motion in many instances in the world;

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

Unit G484: The Newtonian World

Unit G484: The Newtonian World Define linear momentum (and appreciate the vector nature of momentum) net force on a body impulse of a force a perfectly elastic collision an inelastic collision the radian gravitational field strength

More information