Chapter 6: Circular Motion, Orbits, and Gravity Tuesday, September 17, :00 PM. Circular Motion. Rotational kinematics

Size: px
Start display at page:

Download "Chapter 6: Circular Motion, Orbits, and Gravity Tuesday, September 17, :00 PM. Circular Motion. Rotational kinematics"

Transcription

1 Ch6 Page 1 Chapter 6: Circular Motion, Orbits, and Gravity Tuesday, September 17, :00 PM Circular Motion Rotational kinematics We'll discuss the basics of rotational kinematics in this chapter; the kinematics equations for constant angular acceleration are discussed in Chapter 7. The basic quantities of rotational kinematics are angular position, angular displacement, angular velocity, and angular acceleration. angular position measured in degrees or radians review of angle measure in degrees and radians; remember that the radian is a "unitless" unit Remember that for a complete circle, the circumference is and therefore the angle of a complete circle is But we know that for a complete circle, = 360. Thus,

2 Ch6 Page 2 Using these two conversion factors allows one to convert from degrees to radians, or vice versa. For example, Angular displacement and angular velocity Connecting linear and angular kinematic quantities

3 Ch6 Page 3

4 Ch6 Page 4

5 Ch6 Page 5 Example: maximum speed for a car turning around a curve on a level road with friction A car of mass 1200 kg moves around a curve on level ground that has a a radius of 20 m. Determine the maximum speed for which the car can safely move around the curve. The coefficient of friction is 0.5.

6 Ch6 Page 6 Thus, the maximum acceleration that friction between the tires and the road can produce is 4.9 m/s 2. Notice that the maximum safe speed through the curve is independent of the mass of the vehicle; thus, a speed limit sign can be used that is appropriate for all vehicles, whether they are light motorcycles or heavy transport trucks. Example: banking angle for a highway curve Determine the ideal banking angle for a highway curve that has a (horizontal) radius of 20 m. Suppose that the typical driving speed around the curve is about equal to the speed determined in the previous example. Solution: There is no friction on the road; presumably it's very icy.

7 Notice that the ideal banking angle is independent of the mass of the vehicle; this is nice. It means that one can design a banked highway that will be appropriate for all vehicles, no matter their mass, so it will be just as safe for light motorcycles and heavy transport trucks. Ch6 Page 7

8 Ch6 Page 8 Example: apparent weight for motion in a vertical circle Consider a car going around a vertical "loop-the-loop" of radius 3 m. Determine the minimum speed the car needs to make it through the loop. Alternatively: Consider a bucket of water spinning in a vertical circle and determine the minimum speed (or angular speed) so that the water does not fall out of the bucket. Solution: Draw a free-body diagram for the car when it is at the top of the loop: This means that if the car is to complete the circle, the force must be provided by the normal force from the loop and gravity. As the speed increases, the normal force has to increase to provide the necessary force. On the other hand, if the speed of the car decreases, then the normal force will also decrease, until at a critical speed, the weight of the car will be sufficient to provide the centripetal force. If the speed were to decrease below this critical minimum value, the car will leave the loop and crash down. Thus, the minimum speed for the car to make it through the loop corresponds to n = 0. Setting n = 0 and solving for the speed of the car, we obtain:

9 Ch6 Page 9 This may not seem like a very high speed, but remember that the loop is not very big. I once saw a "cirque" stunt where motorcycles were flying around the inside of a spherical metal structure, and the radius might have been this big and the speeds seemed about this fast or a bit faster. For a much bigger loop, a larger speed is required. Now solve the problem of the water in the bucket yourself. How fast do you have to swing a bucket around so that the water doesn't fall out? centrifuges Read about centrifuges in the text book; they provide a nice practical example of circular motion. (Also, you'll think about physics the next time you use a lettuce spinner, which is a sort of centrifuge.) Newton's law of gravity Example: gravitational force between Earth and Moon

10 Ch6 Page 10 Newton's law of gravity is an inverse-square force law, and has the same structure as Coulomb's law for the force between two charged particles at rest. The diagram above is intended to illustrate that the force decreases by a factor of 4 when the distance between the objects doubles. Example: gravitational force between Earth and a small object of mass m at the Earth's surface

11 Ch6 Page 11 This provides insight into our assumption earlier in the course that the acceleration due to gravity g is constant; we can see by the previous equation that this is not exactly true. Close to the Earth's surface it is approximately true, but as you move away from the Earth's surface the value of the acceleration due to gravity decreases. The equation above also gives us a way to "weigh" the Earth. The acceleration due to gravity can be measured in a laboratory (in fact you did so in the pendulum experiment in this course), and so can the gravitational constant G (look up the famous Cavendish experiment for details). The radius of the Earth can be determined using an ingenious geometrical method first devised by Eratosthenes (you can also look this up); then the previous equation can be solved for the mass of the Earth. The same formula can be used to determine the acceleration due to gravity on other planets, moons, asteroids, etc. Just replace the mass and radius of Earth by the mass and radius of the other planet. Also note that some books call the acceleration due to gravity at the surface (i.e., "g") by the term "surface gravity." orbital motion of a satellite around Earth direction of gravitational forces at various points of the orbit gravitational acceleration is approximately constant near surface, but the direction is clearly not constant over larger scales, nor is the magnitude constant over larger scales

12 Ch6 Page 12 Weightlessness in space satellites in orbit are in free fall hence occupants are weightless check the textbook for details Kepler's third law of planetary motion Using Newton's law of gravity and Newton's second law of motion, we can derive Kepler's third law of planetary motion.

13 Ch6 Page 13 If the orbit of the planet is elliptical instead of circular, a more complex analysis shows that Kepler's third law is still valid provided that we use the "semi-major axis" of the orbit in place of r. The semi-major axis of the elliptical orbit is the distance from the centre of the ellipse to the most distant point on the orbit. Example: Use Kepler's third law of planetary motion to determine the distance between the Earth and Sun, given that the mass of the Sun is about kg. Solution: Make sure to convert the period of the Earth into seconds:

14 Ch6 Page 14 Dark matter: One of today's unsolved puzzles about the universe As we discussed in class, if you are deep below the surface of the Earth, let's say in a very deep mine shaft, your weight is less than at the surface of the Earth. Only the mass "interior" to you (i.e., at radii smaller than yours) is effective in exerting a force on you; the force exerted on you by the mass of the Earth that is at larger radii cancels. This means that if you were anywhere inside a hollow spherical shell of mass, provided the shell has constant density, the gravitational force on you is zero. (If you wish to learn more about this, look up "Gauss's law" for gravity (there is a version of Gauss's law for electrostatic forces as well); to understand the mathematical argument, you'll need to have some integral calculus under your belt.) The same principle can be applied to the motions of stars in our galaxy. If you analyze the motion of stars at various positions in our galaxy, you can deduce the amount of mass in the galaxy that lies closer to the galactic centre than the given star (using Newton's law of gravity and Newton's laws of motion). Repeating this kind of analysis for many stars gives us a good idea for the distribution of mass in the galaxy. And this leads to a puzzle: The amount of mass that we detect by usual means (regular light telescopes, radio telescopes, etc.) is nowhere near enough to account for the mass that we know must be there by analyzing motions in the galaxy. That is, the "visual matter" does not account for all the matter that must be present; there must be some "dark matter." What on Earth can this dark matter be? Nobody knows. It is highly unlikely that it could be simply ordinary matter that can't be detected (such as "cold" dust particles or gas, abandoned TV sets, etc.), so scientists have turned to more speculative possibilities. Maybe dark matter is some exotic new form of matter. If so, such forms of matter have not been detected in laboratories, which leaves us no closer to resolving the puzzle. This is an example of the type of unresolved puzzle that is found at the frontier of every branch of science. There are always unsolved

15 Ch6 Page 15 puzzles, which means there is always room for new ideas, and creative researchers have plenty of opportunities for making interesting new discoveries. Maybe one of you will devote the time and work necessary to reach one of the research frontiers; it will take a lot of time and work to reach the frontier, but for the right kind of person (i.e., one who is persistent and willing to put up with a certain amount of failure and frustration) the journey will be a lot of fun and very satisfying. Geostationary satellite orbits It's convenient to have communications satellites that orbit Earth above its equator with a period equal to Earth's rotational period; in this way, they "hover" over the same geographical point on Earth. Using Kepler's third law we can calculate the radius of the orbit of such "geostationary" satellites. This is the distance from the centre of the Earth, so the distance of such a satellite from the surface of the Earth is 6400 km less, which is 35,850 km above the Earth's surface. The International Space Station orbits Earth at an altitude of about 400 km, which is considered "low Earth orbit;" geosynchronous satellites are in "high Earth orbit." Additional exercises: Page 196, Exercise 7: A turntable rotates counterclockwise at 78 rpm. A

16 Ch6 Page 16 speck of dust on the turntable is at = 0.45 rad at t = 0 s. Determine the angle of the speck at t = 8.0 s. (The result should be between 0 and 2.) Solution: Page 197, Exercise 27: A satellite orbiting the Moon very near the surface has a period of 110 min. Use this information, together with the radius of the Moon (which is m), and the mass of the Moon (which is kg), to calculate the free-fall acceleration on the Moon's surface. Solution:

17 Ch6 Page 17 This means that the surface gravity (which is another word for the free-fall acceleration at the surface) on the Moon is about 1/6 as much as the surface gravity on the Earth. How would this change life for you if you lived on the Moon for a while? Page 197, Exercise 45: A 500 g ball swings in a vertical circle at the end of a 1.5-m-long string. When the ball is at the bottom of the circle, the tension in the string is 15 N. Determine the speed of the ball at this point. Solution:

Let's first discuss the period and frequency for circular motion: period T: amount of time needed to complete one revolution (unit: s, min, h, etc.

Let's first discuss the period and frequency for circular motion: period T: amount of time needed to complete one revolution (unit: s, min, h, etc. Chapter 5: Dynamics of Uniform Circular Motion Tuesday, September 17, 2013 10:00 PM Rotational kinematics We'll discuss the basics of rotational kinematics in this chapter; the kinematics equations for

More information

review of angle measure in degrees and radians; remember that the radian is a "unitless" unit

review of angle measure in degrees and radians; remember that the radian is a unitless unit Ch6 Page 1 Chapter 6: Circular Motion, Orbits, and Gravity Tuesday, September 17, 2013 10:00 PM Circular Motion rotational kinematics angular position measured in degrees or radians review of angle measure

More information

Let's first discuss the period and frequency for circular motion: period T: amount of time needed to complete one revolution (unit: s, min, h, etc.

Let's first discuss the period and frequency for circular motion: period T: amount of time needed to complete one revolution (unit: s, min, h, etc. Chapter 5: Dynamics of Uniform Circular Motion Tuesday, September 17, 2013 10:00 PM Rotational Kinematics We'll discuss the basics of rotational kinematics in this chapter; the kinematics equations for

More information

Proficient. a. The gravitational field caused by a. The student is able to approximate a numerical value of the

Proficient. a. The gravitational field caused by a. The student is able to approximate a numerical value of the Unit 6. Circular Motion and Gravitation Name: I have not failed. I've just found 10,000 ways that won't work.-- Thomas Edison Big Idea 1: Objects and systems have properties such as mass and charge. Systems

More information

Circular Motion and Gravitation Notes 1 Centripetal Acceleration and Force

Circular Motion and Gravitation Notes 1 Centripetal Acceleration and Force Circular Motion and Gravitation Notes 1 Centripetal Acceleration and Force This unit we will investigate the special case of kinematics and dynamics of objects in uniform circular motion. First let s consider

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

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

Circular Motion & Gravitation FR Practice Problems

Circular Motion & Gravitation FR Practice Problems 1) A mass m is attached to a length L of string and hung straight strainght down from a pivot. Small vibrations at the pivot set the mass into circular motion, with the string making an angle θ with the

More information

Chapter 5 Circular Motion; Gravitation

Chapter 5 Circular Motion; Gravitation Chapter 5 Circular Motion; Gravitation Units of Chapter 5 Kinematics of Uniform Circular Motion Dynamics of Uniform Circular Motion Highway Curves, Banked and Unbanked Newton s Law of Universal Gravitation

More information

Chapter 5 Circular Motion; Gravitation

Chapter 5 Circular Motion; Gravitation Chapter 5 Circular Motion; Gravitation Units of Chapter 5 Kinematics of Uniform Circular Motion Dynamics of Uniform Circular Motion Highway Curves, Banked and Unbanked Nonuniform Circular Motion Centrifugation

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

Announcements 15 Oct 2013

Announcements 15 Oct 2013 Announcements 15 Oct 2013 1. While you re waiting for class to start, see how many of these blanks you can fill out. Tangential Accel.: Direction: Causes speed to Causes angular speed to Therefore, causes:

More information

12/1/2014. Chapter 5 Circular Motion; Gravitation. Contents of Chapter 5. Contents of Chapter Kinematics of Uniform Circular Motion

12/1/2014. Chapter 5 Circular Motion; Gravitation. Contents of Chapter 5. Contents of Chapter Kinematics of Uniform Circular Motion Lecture PowerPoints Chapter 5 Physics: Principles with Applications, 7 th edition Giancoli Chapter 5 Circular Motion; Gravitation This work is protected by United States copyright laws and is provided

More information

Circular Motion and Gravitation Notes 1 Centripetal Acceleration and Force

Circular Motion and Gravitation Notes 1 Centripetal Acceleration and Force Circular Motion and Gravitation Notes 1 Centripetal Acceleration and Force This unit we will investigate the special case of kinematics and dynamics of objects in uniform circular motion. First let s consider

More information

Chapter 6: Uniform Circular Motion and Gravity

Chapter 6: Uniform Circular Motion and Gravity Chapter 6: Uniform Circular Motion and Gravity Brent Royuk Phys-111 Concordia University Angular Measure Angular distance: Δθ = θ - θ o Analogous to linear distance Rotation instead of translation How

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

Lecture Presentation. Chapter 6 Preview Looking Ahead. Chapter 6 Circular Motion, Orbits, and Gravity

Lecture Presentation. Chapter 6 Preview Looking Ahead. Chapter 6 Circular Motion, Orbits, and Gravity Chapter 6 Preview Looking Ahead Lecture Presentation Chapter 6 Circular Motion, Orbits, and Gravity Text: p. 160 Slide 6-2 Chapter 6 Preview Looking Back: Centripetal Acceleration In Section 3.8, you learned

More information

Physics 12. Unit 5 Circular Motion and Gravitation Part 2

Physics 12. Unit 5 Circular Motion and Gravitation Part 2 Physics 12 Unit 5 Circular Motion and Gravitation Part 2 1. Newton s law of gravitation We have seen in Physics 11 that the force acting on an object due to gravity is given by a well known formula: F

More information

PHYSICS. Chapter 8 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT Pearson Education, Inc.

PHYSICS. Chapter 8 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT Pearson Education, Inc. PHYSICS FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E Chapter 8 Lecture RANDALL D. KNIGHT Chapter 8. Dynamics II: Motion in a Plane IN THIS CHAPTER, you will learn to solve problems about motion

More information

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

Circular Motion and Gravitation. Centripetal Acceleration

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

More information

Chapter 6 Circular Motion, Orbits and Gravity

Chapter 6 Circular Motion, Orbits and Gravity Chapter 6 Circular Motion, Orbits and Gravity Topics: The kinematics of uniform circular motion The dynamics of uniform circular motion Circular orbits of satellites Newton s law of gravity Sample question:

More information

S Notre Dame 1

S Notre Dame 1 Worksheet 1 Horizontal Circular Motion 1. Will the acceleration of a car be the same if it travels Around a sharp curve at 60 km/h as when it travels around a gentle curve at the same speed? Explain. 2.

More information

Circular Motion PreTest

Circular Motion PreTest Circular Motion PreTest Date: 06/03/2008 Version #: 0 Name: 1. In a series of test runs, a car travels around the same circular track at different velocities. Which graph best shows the relationship between

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

Physics General Physics. Lecture 8 Planetary Motion. Fall 2016 Semester Prof. Matthew Jones

Physics General Physics. Lecture 8 Planetary Motion. Fall 2016 Semester Prof. Matthew Jones Physics 22000 General Physics Lecture 8 Planetary Motion Fall 2016 Semester Prof. Matthew Jones 1 First Midterm Exam Tuesday, October 4 th, 8:00-9:30 pm Location: PHYS 112 and WTHR 200. Covering material

More information

PHYSICS - CLUTCH CH 06: CENTRIPETAL FORCES & GRAVITATION.

PHYSICS - CLUTCH CH 06: CENTRIPETAL FORCES & GRAVITATION. !! www.clutchprep.com UNIFORM CIRCULAR MOTION In Uniform Circular Motion, an object moves with constant speed in a circular path. v,t = a,c = a,c = v,t 2 / r r = When an object completes one lap ( or ),

More information

Chapter 13. Gravitation. PowerPoint Lectures for University Physics, 14th Edition Hugh D. Young and Roger A. Freedman Lectures by Jason Harlow

Chapter 13. Gravitation. PowerPoint Lectures for University Physics, 14th Edition Hugh D. Young and Roger A. Freedman Lectures by Jason Harlow Chapter 13 Gravitation PowerPoint Lectures for University Physics, 14th Edition Hugh D. Young and Roger A. Freedman Lectures by Jason Harlow Next one week Today: Ch 13 Wed: Review of Ch 8-11, focusing

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

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

Lecture PowerPoints. Chapter 6 Physics for Scientists and Engineers, with Modern Physics, 4 th edition Giancoli

Lecture PowerPoints. Chapter 6 Physics for Scientists and Engineers, with Modern Physics, 4 th edition Giancoli Lecture PowerPoints Chapter 6 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

Chapter 12 Gravity. Copyright 2010 Pearson Education, Inc.

Chapter 12 Gravity. Copyright 2010 Pearson Education, Inc. Chapter 12 Gravity Units of Chapter 12 Newton s Law of Universal Gravitation Gravitational Attraction of Spherical Bodies Kepler s Laws of Orbital Motion Gravitational Potential Energy Energy Conservation

More information

Chapter 9. Gravitation

Chapter 9. Gravitation Chapter 9 Gravitation 9.1 The Gravitational Force For two particles that have masses m 1 and m 2 and are separated by a distance r, the force has a magnitude given by the same magnitude of force acts on

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

No Brain Too Small PHYSICS

No Brain Too Small PHYSICS MECHANICS: CIRCULAR MOTION QUESTIONS CIRCULAR MOTION (2016;1) Alice is in a car on a ride at a theme park. The car travels along a circular track that is banked, as shown in the diagram. On the diagram,

More information

(b) The period T and the angular frequency ω of uniform rotation are related to the cyclic frequency f as. , ω = 2πf =

(b) The period T and the angular frequency ω of uniform rotation are related to the cyclic frequency f as. , ω = 2πf = PHY 302 K. Solutions for problem set #9. Non-textbook problem #1: (a) Rotation frequency of 1 Hz means one revolution per second, or 60 revolutions per minute (RPM). The pre-lp vinyl disks rotated at 78

More information

AP Unit 8: Uniform Circular Motion and Gravity HW

AP Unit 8: Uniform Circular Motion and Gravity HW Basics 1D Mot. 2D Mot. Forces Energy Moment. Rotation Circ/Grav SHM Waves Circuits AP Unit 8: Uniform Circular Motion and Gravity HW AP Exam Knowledge & Skills (What skills are needed to achieve the desired

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

Welcome back to Physics 211

Welcome back to Physics 211 Welcome back to Physics 211 Today s agenda: Circular motion Impulse and momentum 08-2 1 Current assignments Reading: Chapter 9 in textbook Prelecture due next Thursday HW#8 due NEXT Friday (extension!)

More information

AP Physics C - Problem Drill 18: Gravitation and Circular Motion

AP Physics C - Problem Drill 18: Gravitation and Circular Motion AP Physics C - Problem Drill 18: Gravitation and Circular Motion Question No. 1 of 10 Instructions: (1) Read the problem and answer choices carefully () Work the problems on paper as 1. Two objects some

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

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

An object moving in a circle with radius at speed is said to be undergoing.

An object moving in a circle with radius at speed is said to be undergoing. Circular Motion Study Guide North Allegheny High School Mr. Neff An object moving in a circle with radius at speed is said to be undergoing. In this case, the object is because it is constantly changing

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

Outline for Today: Newton s Law of Universal Gravitation The Gravitational Field Orbital Motion Gravitational Potential Energy. Hello!

Outline for Today: Newton s Law of Universal Gravitation The Gravitational Field Orbital Motion Gravitational Potential Energy. Hello! PHY131H1F - Class 13 Outline for Today: Newton s Law of Universal Gravitation The Gravitational Field Orbital Motion Gravitational Potential Energy Under the Flower of Kent apple tree in the Woolsthorpe

More information

Preview. Circular Motion and Gravitation Section 1. Section 1 Circular Motion. Section 2 Newton s Law of Universal Gravitation

Preview. Circular Motion and Gravitation Section 1. Section 1 Circular Motion. Section 2 Newton s Law of Universal Gravitation Circular Motion and Gravitation Section 1 Preview Section 1 Circular Motion Section 2 Newton s Law of Universal Gravitation Section 3 Motion in Space Section 4 Torque and Simple Machines Circular Motion

More information

Advanced Higher Physics. Rotational motion

Advanced Higher Physics. Rotational motion Wallace Hall Academy Physics Department Advanced Higher Physics Rotational motion Problems AH Physics: Rotational Motion 1 2013 Data Common Physical Quantities QUANTITY SYMBOL VALUE Gravitational acceleration

More information

The Force of Gravity exists between any two masses! Always attractive do you feel the attraction? Slide 6-35

The Force of Gravity exists between any two masses! Always attractive do you feel the attraction? Slide 6-35 The Force of Gravity exists between any two masses! Always attractive do you feel the attraction? Slide 6-35 Summary Newton s law of gravity describes the gravitational force between A. the earth and the

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

Problem Solving Circular Motion Dynamics Challenge Problems

Problem Solving Circular Motion Dynamics Challenge Problems Problem 1: Double Star System Problem Solving Circular Motion Dynamics Challenge Problems Consider a double star system under the influence of gravitational force between the stars. Star 1 has mass m 1

More information

AP Physics 1 Lesson 10.a Law of Universal Gravitation Homework Outcomes

AP Physics 1 Lesson 10.a Law of Universal Gravitation Homework Outcomes AP Physics 1 Lesson 10.a Law of Universal Gravitation Homework Outcomes 1. Use Law of Universal Gravitation to solve problems involving different masses. 2. Determine changes in gravitational and kinetic

More information

Chapter 6 UNIFORM CIRCULAR MOTION AND GRAVITATION

Chapter 6 UNIFORM CIRCULAR MOTION AND GRAVITATION Chapter 6 UNIFORM CIRCULAR MOTION AND GRAVITATION An object moving in a circle must have a force acting on it; otherwise it would move in a straight line. The direction of the force is towards the center

More information

Cutnell/Johnson Physics

Cutnell/Johnson Physics Cutnell/Johnson Physics Classroom Response System Questions Chapter 5 Dynamics of Uniform Circular Motion Interactive Lecture Questions 5.1.1. An airplane flying at 115 m/s due east makes a gradual turn

More information

PHYSICS. Chapter 8 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT Pearson Education, Inc.

PHYSICS. Chapter 8 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT Pearson Education, Inc. PHYSICS FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E Chapter 8 Lecture RANDALL D. KNIGHT Chapter 8. Dynamics II: Motion in a Plane IN THIS CHAPTER, you will learn to solve problems about motion

More information

Honors Assignment - Circular and Periodic Motion

Honors Assignment - Circular and Periodic Motion Honors Assignment - Circular and Periodic Motion Reading: Chapter 5, and 11 1 through 11 5 Objectives/HW: Assignment #1 M: # 1 6 Assignment #2 M: # 7 15 Assignment #3 Text: Chap 5 # 6, 12 M: # 17 22 Assignment

More information

Preview. Circular Motion and Gravitation Section 1. Section 1 Circular Motion. Section 2 Newton s Law of Universal Gravitation

Preview. Circular Motion and Gravitation Section 1. Section 1 Circular Motion. Section 2 Newton s Law of Universal Gravitation Circular Motion and Gravitation Section 1 Preview Section 1 Circular Motion Section 2 Newton s Law of Universal Gravitation Section 3 Motion in Space Section 4 Torque and Simple Machines Circular Motion

More information

Name St. Mary's HS AP Physics Circular Motion HW

Name St. Mary's HS AP Physics Circular Motion HW Name St. Mary's HS AP Physics Circular Motion HW Base your answers to questions 1 and 2 on the following situation. An object weighing 10 N swings at the end of a rope that is 0.72 m long as a simple pendulum.

More information

Circular Orbits. Slide Pearson Education, Inc.

Circular Orbits. Slide Pearson Education, Inc. Circular Orbits The figure shows a perfectly smooth, spherical, airless planet with one tower of height h. A projectile is launched parallel to the ground with speed v 0. If v 0 is very small, as in trajectory

More information

Lecture Presentation Chapter 6 Circular Motion, Orbits, and Gravity

Lecture Presentation Chapter 6 Circular Motion, Orbits, and Gravity Lecture Presentation Chapter 6 Circular Motion, Orbits, and Gravity Suggested Videos for Chapter 6 Prelecture Videos Forces and Apparent Forces Solving Circular Motion Problems Orbits and Gravity Class

More information

Assignment - Periodic Motion. Reading: Giancoli, Chapter 5 Holt, Chapter 7. Objectives/HW:

Assignment - Periodic Motion. Reading: Giancoli, Chapter 5 Holt, Chapter 7. Objectives/HW: Assignment - Periodic Motion Reading: Giancoli, Chapter 5 Holt, Chapter 7 Objectives/HW: The student will be able to: 1 Define and calculate period and frequency. 2 Apply the concepts of position, distance,

More information

Physics 161 Lecture 10: Universal Gravitation. October 4, /6/20 15

Physics 161 Lecture 10: Universal Gravitation. October 4, /6/20 15 Physics 161 Lecture 10: Universal Gravitation October 4, 2018 1 Midterm announcements 1) The first midterm exam will be Thursday October 18 from 10:00 pm to 11:20 pm in ARC- 103. 2) The exam will be multiple

More information

Circular Motion 1

Circular Motion 1 --------------------------------------------------------------------------------------------------- Circular Motion 1 ---------------------------------------------------------------------------------------------------

More information

DEVIL CHAPTER 6 TEST REVIEW

DEVIL CHAPTER 6 TEST REVIEW IB PHYSICS Name: Period: Date: # Marks: 51 DEVIL PHYSICS BADDEST CLASS ON CAMPUS CHAPTER 6 TEST REVIEW 1. A cyclist rides around a circular track at a uniform speed. Which of the following correctly gives

More information

Multiple Choice Portion

Multiple Choice Portion Unit 5: Circular Motion and Gravitation Please Note that the gravitational potential energy questions are located in Unit 4 (Energy etc.) Multiple Choice Portion 1. What is the centripetal acceleration

More information

Outline for Today: Newton s Law of Universal Gravitation The Gravitational Field Orbital Motion Gravitational Potential Energy

Outline for Today: Newton s Law of Universal Gravitation The Gravitational Field Orbital Motion Gravitational Potential Energy PHY131H1F - Class 13 Outline for Today: Newton s Law of Universal Gravitation The Gravitational Field Orbital Motion Gravitational Potential Energy Under the Flower of Kent apple tree in the Woolsthorpe

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

Crash Course: Uniform Circular Motion. Our next test will be the week of Nov 27 Dec 1 and will cover projectiles and circular motion.

Crash Course: Uniform Circular Motion. Our next test will be the week of Nov 27 Dec 1 and will cover projectiles and circular motion. Curriculum Outcomes Circular Motion (8 hours) describe uniform circular motion using algebraic and vector analysis (325 12) explain quantitatively circular motion using Newton s laws (325 13) Crash Course:

More information

Chapter 8. Dynamics II: Motion in a Plane

Chapter 8. Dynamics II: Motion in a Plane Chapter 8. Dynamics II: Motion in a Plane Chapter Goal: To learn how to solve problems about motion in a plane. Slide 8-2 Chapter 8 Preview Slide 8-3 Chapter 8 Preview Slide 8-4 Chapter 8 Preview Slide

More information

Copyright 2010 Pearson Education, Inc. GRAVITY. Chapter 12

Copyright 2010 Pearson Education, Inc. GRAVITY. Chapter 12 GRAVITY Chapter 12 Units of Chapter 12 Newton s Law of Universal Gravitation Gravitational Attraction of Spherical Bodies Kepler s Laws of Orbital Motion Gravitational Potential Energy Energy Conservation

More information

Radial Acceleration. recall, the direction of the instantaneous velocity vector is tangential to the trajectory

Radial Acceleration. recall, the direction of the instantaneous velocity vector is tangential to the trajectory Radial Acceleration recall, the direction of the instantaneous velocity vector is tangential to the trajectory 1 Radial Acceleration recall, the direction of the instantaneous velocity vector is tangential

More information

This Week. 2/3/14 Physics 214 Fall

This Week. 2/3/14 Physics 214 Fall This Week Circular motion Going round the bend Riding in a ferris wheel, the vomit comet Gravitation Our solar system, satellites (Direct TV) The tides, Dark matter, Space Elevator 2/3/14 Physics 214 Fall

More information

Chapter 6 Gravitation and Newton s Synthesis

Chapter 6 Gravitation and Newton s Synthesis Chapter 6 Gravitation and Newton s Synthesis If the force of gravity is being exerted on objects on Earth, what is the origin of that force? Newton s realization was that the force must come from the Earth.

More information

Downloaded from

Downloaded from Chapter 8 (Gravitation) Multiple Choice Questions Single Correct Answer Type Q1. The earth is an approximate sphere. If the interior contained matter which is not of the same density everywhere, then on

More information

Universal gravitation

Universal gravitation Universal gravitation Physics 211 Syracuse University, Physics 211 Spring 2015 Walter Freeman February 22, 2017 W. Freeman Universal gravitation February 22, 2017 1 / 14 Announcements Extra homework help

More information

2010 Pearson Education, Inc. Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity

2010 Pearson Education, Inc. Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity 4.1 Describing Motion: Examples from Daily Life Some of the topics we will explore: How do we describe motion? (Speed,

More information

4 th week of Lectures Jan. 29. Feb

4 th week of Lectures Jan. 29. Feb 4 th week of Lectures Jan. 29. Feb. 02. 2018. Circular motion Going around the bend Riding in a Ferris wheel Gravitation Our solar system, satellites The tides 1/31/2018 Physics 214 Spring 2018 1 The Greatest

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 6 Review Answer Key

Chapter 6 Review Answer Key Chapter 6 Review Answer Key Understanding Vocabulary 1. displacement 2. trajectory 3. projectile 4. parabola 5. range 6. revolves 7. rotates 8. angular speed 9. centripetal force 10. law of universal gravitation

More information

This Week. 7/29/2010 Physics 214 Fall

This Week. 7/29/2010 Physics 214 Fall This Week Circular motion Going round the bend Riding in a ferris wheel, the vomit comet Gravitation Our solar system, satellites (Direct TV) The tides, Dark matter, Space Elevator 7/29/2010 Physics 214

More information

1 The displacement, s in metres, of an object after a time, t in seconds, is given by s = 90t 4 t 2

1 The displacement, s in metres, of an object after a time, t in seconds, is given by s = 90t 4 t 2 CFE Advanced Higher Physics Unit 1 Rotational Motion and Astrophysics Kinematic relationships 1 The displacement, s in metres, of an object after a time, t in seconds, is given by s = 90t 4 t 2 a) Find

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

Gravity. James H Dann, Ph.D. Say Thanks to the Authors Click (No sign in required)

Gravity. James H Dann, Ph.D. Say Thanks to the Authors Click   (No sign in required) Gravity James H Dann, Ph.D. Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) To access a customizable version of this book, as well as other interactive content, visit

More information

Make sure that you are able to operate with vectors rapidly and accurately. Practice now will pay off in the rest of the course.

Make sure that you are able to operate with vectors rapidly and accurately. Practice now will pay off in the rest of the course. Ch3 Page 1 Chapter 3: Vectors and Motion in Two Dimensions Tuesday, September 17, 2013 10:00 PM Vectors are useful for describing physical quantities that have both magnitude and direction, such as position,

More information

TYPICAL NUMERIC QUESTIONS FOR PHYSICS I REGULAR QUESTIONS TAKEN FROM CUTNELL AND JOHNSON CIRCULAR MOTION CONTENT STANDARD IB

TYPICAL NUMERIC QUESTIONS FOR PHYSICS I REGULAR QUESTIONS TAKEN FROM CUTNELL AND JOHNSON CIRCULAR MOTION CONTENT STANDARD IB TYPICAL NUMERIC QUESTIONS FOR PHYSICS I REGULAR QUESTIONS TAKEN FROM CUTNELL AND JOHNSON CIRCULAR MOTION CONTENT STANDARD IB 1. A car traveling at 20 m/s rounds a curve so that its centripetal acceleration

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

Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity. Copyright 2009 Pearson Education, Inc.

Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity. Copyright 2009 Pearson Education, Inc. Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity How do we describe motion? Precise definitions to describe motion: Speed: Rate at which object moves speed = distance time

More information

Chapter 4 Circular Motion and Gravitation Planetary Data Homework # 26

Chapter 4 Circular Motion and Gravitation Planetary Data Homework # 26 Planetary Data Homework # 26 PLANETARY DATA Mean Distance Mass from Sun Radius Period Planet (kg) (m) (m) (days) Sun 1.99 x 10 30 6.970 x 10 8 Mercury 3.30 x 10 23 5.791 x 10 10 2.439 x 10 6 87.97 Venus

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

PH201 Chapter 6 Solutions

PH201 Chapter 6 Solutions PH201 Chapter 6 Solutions 6.2. Set Up: Since the stone travels in a circular path, its acceleration is directed toward the center of the circle. The only horizontal force on the stone is the tension of

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

SAPTARSHI CLASSES PVT. LTD.

SAPTARSHI CLASSES PVT. LTD. SAPTARSHI CLASSES PVT. LTD. NEET/JEE Date : 13/05/2017 TEST ID: 120517 Time : 02:00:00 Hrs. PHYSICS, Chem Marks : 360 Phy : Circular Motion, Gravitation, Che : Halogen Derivatives Of Alkanes Single Correct

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

A = 6561 times greater. B. 81 times greater. C. equally strong. D. 1/81 as great. E. (1/81) 2 = 1/6561 as great Pearson Education, Inc.

A = 6561 times greater. B. 81 times greater. C. equally strong. D. 1/81 as great. E. (1/81) 2 = 1/6561 as great Pearson Education, Inc. Q13.1 The mass of the Moon is 1/81 of the mass of the Earth. Compared to the gravitational force that the Earth exerts on the Moon, the gravitational force that the Moon exerts on the Earth is A. 81 2

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

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 Chapter 8 Lecture a strategic approach randall d. knight FOR SCIENTISTS AND ENGINEERS CHAPTER8_LECTURE8.1 THIRD EDITION

physics Chapter 8 Lecture a strategic approach randall d. knight FOR SCIENTISTS AND ENGINEERS CHAPTER8_LECTURE8.1 THIRD EDITION Chapter 8 Lecture physics FOR SCIENTISTS AND ENGINEERS a strategic approach THIRD EDITION randall d. knight CHAPTER8_LECTURE8.1 2013 Pearson Education, Inc. 1 Chapter 8. Newton s Laws for Circular Motion

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

Making Sense of the Universe (Chapter 4) Why does the Earth go around the Sun? Part, but not all, of Chapter 4

Making Sense of the Universe (Chapter 4) Why does the Earth go around the Sun? Part, but not all, of Chapter 4 Making Sense of the Universe (Chapter 4) Why does the Earth go around the Sun? Part, but not all, of Chapter 4 Based on part of Chapter 4 This material will be useful for understanding Chapters 8 and 11

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

Chapter 7. Preview. Objectives Tangential Speed Centripetal Acceleration Centripetal Force Describing a Rotating System. Section 1 Circular Motion

Chapter 7. Preview. Objectives Tangential Speed Centripetal Acceleration Centripetal Force Describing a Rotating System. Section 1 Circular Motion Section 1 Circular Motion Preview Objectives Tangential Speed Centripetal Acceleration Centripetal Force Describing a Rotating System Section 1 Circular Motion Objectives Solve problems involving centripetal

More information