CIRCULAR MOTION AND GRAVITATION

Size: px
Start display at page:

Download "CIRCULAR MOTION AND GRAVITATION"

Transcription

1 CIRCULAR MOTION AND GRAVITATION An object moves in a straight line if the net force on it acts in the direction of motion, or is zero. If the net force acts at an angle to the direction of motion at any moment, then the object moves in a curved path. KINEMATICS OF UNIFORM CIRCULAR MOTION! An object that moves in a circle at constant speed, v, is said to experience uniform circular motion. " The magnitude of the velocity remains constant, but the direction of the velocity is continuously changing. " Since acceleration is defined as the rate of change in velocity, a change in direction of v constitutes an acceleration just as does a change in magnitude. " THUS, an object revolving in a circle is continuously accelerating, even when the speed remains constant.!acceleration is defined as: a = v 2 - v 1 = Δ v Δt Δ t " where Δv is the change in velocity during the short time interval Δ t " Consider a nonzero time interval--during Δt, the particle moves from point A to point B, covering a distance Δl along the arc which subtends an angel Δθ. " Look at figure 5-2 b). Let Δt be VERY small. Then Δl and Δθ are also very small and v 2 will be almost parallel to v 1 and Δv will be essentially perpendicular to them. " Thus, the Δv vector points inward toward the center of the circle and a, by definition above, is in the same direction as Δv, it too must point toward the center of the circle and centripetal acceleration (center-seeking) is born! a.k.a. radial acceleration, a R since it is directed along a radius toward the center of the circle.! To determine the magnitude of a R consider 5-2 a) again. Because CA is to v 1, and CB is to v 2, it follows that the angle Δθ, defined as the angle between CA and CB, is also the angle between v 1 & v 2. " Hence, vectors v 1, v 2, & Δ v form a triangle that is geometrically similar to triangle ABC. " Taking Δθ small (letting Δt be VERY small), we can write Δv Δl where v = v 1 = v 2 since constant velocity v r " This is an exact equality when Δt approaches zero, for then the arc length Δl equals the cord length AB. Since we want to find the instantaneous acceleration, for which Δt approaches zero, we write the above expression as an equality and solve for Δv: Rene McCormick, NMSI. 1

2 Δv = v Δl r To get the centripetal acceleration, a R, we divide Δv by Δt: a R = Δ v = v Δl = v 2 Δt r Δt r and since Δl/Δt is the linear speed, v of the object, CENTRIPETAL ACCELERATION: a R = v 2 SUMMARY: An object moving in a circle of radius r with constant speed v has an acceleration whose direction is toward the center of the circle and whose magnitude is a R = v 2 /r. r " This acceleration depends on v & r. The greater v, the faster the velocity changes direction; and the larger the radius, the less rapidly the velocity changes direction " The acceleration vector points toward the center of the circle. BUT the velocity vector always points in the direction of the motion. " THUS, the v and a vectors are always at every point in the path for uniform circular motion. " Really smashes the notion that a and v are always in the same direction! In projectile motion a = g and is always acting down, now, in circular motion a is to v! " frequency--f, the number of revolutions per second. " period--t, time required for one complete revolution. Equal to 1/f For an object revolving in a constant speed: since in one revolution, the object travels one circumference v = 2π r T Example 5.1 A 150-g ball at the end of a string is revolving uniformly in a horizontal circle of radius m. The ball makes 2.00 revolutions in a second. What is its centripetal acceleration? Rene McCormick, NMSI. 2

3 Example 5.2 The Moon s nearly circular orbit around Earth has a radius of about 384,000 km and a period T of 27.3 days. Determine the acceleration of the Moon toward the Earth. DYNAMICS OF UNIFORM CIRCULAR MOTION According to Newton s Second Law (ΣF = ma), an object that is accelerating must have a net force acting upon it. Yep, we call it centripetal force.! ΣF R = ma R and a R = v 2 /r so... CENTRIPETAL FORCE : ΣF R = ma R = m v 2 and the force is directed toward the center! r! If this net force were not applied, it would obey Newton s first law and fly off in a straight line!! Ever heard of centrifugal (center fleeing) force? Doesn t exist. There is no outward force! " Ever swung an object on a string above your head? The misconception comes from feeling a pull on your hand from the string. This is simply Newton s 3rd law in reaction to the inward force you are putting on the string to keep the object moving in a circle. " If you let go AND there was a centrifugal force acting, then the object would fly OOUTward when you released the string. Doesn t happen--it flies off tangentially to the circular path. Rene McCormick, NMSI. 3

4 Example 5.3 Estimate the force a person must exert on a string attached to a kg ball to make the ball revolve in a horizontal circle of radius m, as in example 5.1. The ball makes 2.00 revolutions per second. Example 5.4 The game of tetherball is played with a ball tied to a pole with a string. When the ball is struck, it whirls around the pole as shown in figure 5-8. In what direction is the acceleration of the ball, and what causes its acceleration? Rene McCormick, NMSI. 4

5 Example 5.5 A kg ball on the end of a 1.10 m-long cord (negligible mass) is swung in a vertical circle. Determine the minimum speed the ball must have at the top of its arc so that it continues moving in a circle. b) Calculate the tension in the cord at the bottom of the arc assuming the ball is moving at twice the speed of part a). Rene McCormick, NMSI. 5

6 Example 5.6 A rider on a Ferris wheel moves in a vertical circle of radius r at a constant speed v. Is the normal force that the seat exerts on the rider at the top of the circle less than, more than, or the same as, the force the seat exerts at the bottom of the circle? A CAR ROUNDING A CURVE Why do you feel thrust outward as a car rounds a curve? You tend to travel in a straight line while the car is traveling in a curved path. The car itself must have an inward force exerted on it if it is to move in a curve. On a flat road, this force is supplied by friction between the tires and the pavement. [It s static friction as long as the tires are not slipping.] If there is not enough friction, the car skids out of a circular path and into a more nearly straight one. Example 5.7 A 1,000 kg car rounds a curve on a flat road of radius 50m at a speed of 50 km/h. Will the car make the turn, or will it skid, if: a) the pavement is dry and μ s = 0.60? b) the pavement is icy and μ s = 0.25? Rene McCormick, NMSI. 6

7 The situation is worse if the wheels lock--stop rotating--when the brakes are applied too hard. As long as the tires are rolling, the bottom of the tire is at rest against the road at each instant, so static friction exists. BUT, if the wheels lock, the tires slide and the friction force, which is now kinetic friction, is less. Moreover, when the road is wet or icy, locking of the wheels occurs with less fore on the brake pedal since there is less road friction to keep the wheels turning rather than sliding. ABS brakes are designed to limit brake pressure just before the point where sliding would occur, by means of delicate sensors and a fast computer--resist the urge to pump the brakes--it causes the sensors and computer to have to start all over each time you pump.! banking--the banking of curves can reduce the chance of skidding because the normal force the road will have a component toward the center of the circle, thus reducing the reliance on friction.! For a given banking angle, θ, there will be a speed for which NO FRICTION at all is required. " This is when the horizontal component of the normal force toward the center of the curve, F N sin θ, is just equal to the force required to give the vehicle its centripetal acceleration. " That is when F N sin θ = m v 2 r Example 5.8 a) For a car traveling with a speed, v, around a curve of radius r, determine a formula for the angle at which a road should be banked so that no friction is required. b) What is this angle for an expressway off-ramp curve of radius 50m at a design speed of 50 km/h? Rene McCormick, NMSI. 7

8 NONUNIFORM CIRCULAR MOTION Circular motion at constant speed occurs when the force is directed toward the center. What if it is directed at an angle like in fig a? The force has 2 components:! The component directed toward the center of the circle gives us F R and gives rise to a R AND keeps the object moving in a circle.! The component tangent to the circle, F tan, acts to increase or decrease the speed, and thus gives rise to a component of the acceleration tangent to the circle a tan.! When the speed of the object is changing, a tangential component of force is acting. " When you first start revolving a ball around your head, you must give it a tangential acceleration. You do this by pulling on the string with your hand displaced from the center of the circle. " The tangential component of the acceleration is equal to the rate of change of the magnitude of the velocity of the object: a tan = Δv Δt " the radial (centripetal) acceleration arises from the change in the direction of the velocity a R = v 2 r " the tangential acceleration always points in a direction tangent to the circle AND is in the direction of the motion IF the speed is increasing and antiparallel IF the speed is decreasing. In any case, a tan & a R are always perpendicular and the total vector acceleration, a is the sum of these two: a ' a 2 tan % a 2 R Example 5.9 A racing car starts from rest in the pit area and accelerates at a uniform rate to a speed of 35 m/s in 11 s, moving on a circular track of radius 500m. Assuming constant tangential acceleration, find a) the tangential acceleration b) the centripetal acceleration when the speed is 30 m/s. Rene McCormick, NMSI. 8

9 NEWTON S LAW OF UNIVERSAL GRAVITATION--noone calls it the 4th! Newton was wondering about the force keeping the Moon in its near circular orbit when an apple fell and bopped him on his noggin. [poetic licence taken] Since falling bodies accelerate, they must have a force acting upon them.! this was met with great resistance since most forces are contact forces--gravitation acts at a distance.! A calculation was in order! " At the Earth s surface, an object is accelerated 9.8 m/s 2 " But, what is the moon s a R? In example 5.2, we found it to be m/s 2 which is 1/3600 g. - That means that the accel. of the Moon toward the Earth is about 1/3600 as great as the acceleration of objects at the Earth s surface " The moon is 384,000 km from the Earth which is about 60 times the Earth s radius of 6380 km. - That means the Moon is 60 times farther from the Earth s center than are objects at the Earth s surface. " BUT 60 x 60 = Again, that number 3600!! Newton concluded that the gravitational force exerted by the Earth on any object decreases with the square of its distance, r from the Earth s center. " The Moon, being 60 Earth s radii away, feels the pull from the center as 1/60 2 = 1/3600 times as strong as if would if it were at the Earth s surface.! Newton also realized that mass mattered! His 3rd law dictates that it be proportional to both masses. Thus, F mem. r 2 Drum roll please... Newton s Law of Universal Gravitation: Every particle in the universe attracts every other particle with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them. This force acts along the line joining the two particles. F = G m 1 m 2 r 2! Henry Cavendish measured G in 1798, about 100 years post Newton.! G = 6.67 x N M2 /kg 2 Rene McCormick, NMSI. 9

10 Example 5.10 A 50 kg person and a 75 kg person are sitting on a bench so that their centers are about 50 cm apart. Estimate the magnitude of the gravitational force each exerts on the other. Example 5.11 What is the force of gravity acting on a 2,000 kg spacecraft when it orbits two Earth radii from the Earth s center (that is, a distance r E = 6380 km above the Earth s surface)? The mass of the Earth is 5.98 x kg. Example 5.12 Find the net force on the Moon ( mass = 7.35 x kg) due to the gravitational attraction of both the Earth and the Sun (mass = 1.99 x kg), assuming they are at right angles to each other? Rene McCormick, NMSI. 10

11 GRAVITY NEAR THE EARTH S SURFACE; GEOPHYSICAL APPLICATIONS Apply Newton s Gravitational Law to an object at the Earth s surface: m 1 becomes m E m 2 becomes m r becomes the distance of the object from the Earth s center or r E = 6.38 x 10 6 m this force is the weight of the object, so... mg = G m m E r E 2 Hence g = G m E r E 2 Until G was measured, the mass of the Earth was not known. Let s calculate: Example 5.13 Estimate the effective value of g on the top of Mt. Everest, 8848 m above the Earth s surface. That is, what is the acceleration due to gravity of objects allowed to fall freely at this altitude? SATELLITES AND WEIGHTLESSNESS How do you get a satellite up? Launch it really fast with a rocket. What keeps a satellite up? Its high tangential speed. Rene McCormick, NMSI. 11

12 If it stops moving, it will crash to Earth. If it moves too fast, it flies off in a straight line path in the same direction as its tangential velocity. For satellites that move in a circle, their acceleration is approx. v 2 /r The force that gives a satellite this acceleration is the force of gravity. Apply Newton s second law: Σ F R = ma R G mm E = m v 2 r 2 r where m is the mass of the satellite. r is the distance of the satellite from the Earth s center and is equal to r E + h h is the height above the Earth s surface Example 5.14 A geosynchronous satellite is one that stays above the same point on the equator of the Earth. Such satellites are used for such purposes as cable TV transmission, for weather forecasting, and as communication relays. Determine a) the height above the Earth s surface such a satellite must orbit b) such a satellite s speed Rene McCormick, NMSI. 12

13 WEIGHTLESSNESS Let s look at a falling elevator. We see an elevator at REST with a bag hanging from a spring scale. The scale reading indicates the downward force exerted on it by the bag which is equal and opposite to the force exerted by the scale upward on the bag. Call this force W. Since the mass, m, is at rest and NOT accelerating, F = ma w-mg = 0 w = mg AND thus as expected! Let s move that elevator! Now F = ma and is NOT equal to zero so... F = ma w-mg = ma w = mg + ma Choosing as + IF acceleration is, w is greater than mg. IF acceleration is, w is less than mg. These are called apparent weights not to be confused with actual weight, mg. Further, if the a = ½ g, then we find w = mg + m ½ g = 1 ½ mg AND we say the bag is experiencing 1 ½ g s. Next, if the a = - ½ g, then we find w = mg - m ½ g = ½ g AND the scale reads ½ the weight. Rene McCormick, NMSI. 13

14 Finally, if the cable breaks and the elevator is in free fall, then a = -g, then we find w = mg + m(-g) = 0 AND voila! APPARENT WEIGHTLESSNESS Satellites are in free fall they are falling toward Earth or they wouldn t be in orbit, they d be travelling in a straight line path according to Newton s first law! Don t confuse with real weightlessness. When a spacecraft is NOT in orbit it is free from the Earth or Moon s gravity and indeed weightless! Rene McCormick, NMSI. 14

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 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

Chapter 5 Part 2. Newton s Law of Universal Gravitation, Satellites, and Weightlessness

Chapter 5 Part 2. Newton s Law of Universal Gravitation, Satellites, and Weightlessness Chapter 5 Part 2 Newton s Law of Universal Gravitation, Satellites, and Weightlessness Newton s ideas about gravity Newton knew that a force exerted on an object causes an acceleration. Most forces occurred

More information

Lecture PowerPoints. Chapter 5 Physics for Scientists & Engineers, with Modern Physics, 4 th edition. Giancoli

Lecture PowerPoints. Chapter 5 Physics for Scientists & Engineers, with Modern Physics, 4 th edition. Giancoli Lecture PowerPoints Chapter 5 Physics for Scientists & Engineers, with Modern Physics, 4 th edition 2009 Pearson Education, Inc. This work is protected by United States copyright laws and is provided solely

More information

Circular Motion 1

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

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

Unit 5 Circular Motion and Gravitation

Unit 5 Circular Motion and Gravitation Unit 5 Circular Motion and Gravitation In the game of tetherball, the struck ball whirls around a pole. In what direction does the net force on the ball point? 1) Tetherball 1) toward the top of the pole

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

Circular Motion.

Circular Motion. 1 Circular Motion www.njctl.org 2 Topics of Uniform Circular Motion (UCM) Kinematics of UCM Click on the topic to go to that section Period, Frequency, and Rotational Velocity Dynamics of UCM Vertical

More information

Circular Motion (Chapter 5)

Circular Motion (Chapter 5) Circular Motion (Chapter 5) So far we have focused on linear motion or motion under gravity (free-fall). Question: What happens when a ball is twirled around on a string at constant speed? Ans: Its velocity

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

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

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 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

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

Uniform Circular Motion. Uniform Circular Motion

Uniform Circular Motion. Uniform Circular Motion Uniform Circular Motion Uniform Circular Motion Uniform Circular Motion An object that moves at uniform speed in a circle of constant radius is said to be in uniform circular motion. Question: Why is uniform

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) You are standing in a moving bus, facing forward, and you suddenly fall forward as the

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

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

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

ASTRONAUT PUSHES SPACECRAFT

ASTRONAUT PUSHES SPACECRAFT ASTRONAUT PUSHES SPACECRAFT F = 40 N m a = 80 kg m s = 15000 kg a s = F/m s = 40N/15000 kg = 0.0027 m/s 2 a a = -F/m a = -40N/80kg = -0.5 m/s 2 If t push = 0.5 s, then v s = a s t push =.0014 m/s, and

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

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Common Quiz Mistakes / Practice for Final Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A ball is thrown directly upward and experiences

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

Algebra Based Physics Uniform Circular Motion

Algebra Based Physics Uniform Circular Motion 1 Algebra Based Physics Uniform Circular Motion 2016 07 20 www.njctl.org 2 Uniform Circular Motion (UCM) Click on the topic to go to that section Period, Frequency and Rotational Velocity Kinematics of

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

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

PRACTICE TEST for Midterm Exam

PRACTICE TEST for Midterm Exam South Pasadena AP Physics PRACTICE TEST for Midterm Exam FORMULAS Name Period Date / / d = vt d = v o t + ½ at 2 d = v o + v 2 t v = v o + at v 2 = v 2 o + 2ad v = v x 2 + v y 2 = tan 1 v y v v x = v cos

More information

Figure 5.1a, b IDENTIFY: Apply to the car. EXECUTE: gives.. EVALUATE: The force required is less than the weight of the car by the factor.

Figure 5.1a, b IDENTIFY: Apply to the car. EXECUTE: gives.. EVALUATE: The force required is less than the weight of the car by the factor. 51 IDENTIFY: for each object Apply to each weight and to the pulley SET UP: Take upward The pulley has negligible mass Let be the tension in the rope and let be the tension in the chain EXECUTE: (a) The

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

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

Physics for Scientist and Engineers third edition Newton s Laws. Example Problem. Variables. Drawing. Solution. Answer: O, 10 N, 20 N, 38N, 39N, 29N

Physics for Scientist and Engineers third edition Newton s Laws. Example Problem. Variables. Drawing. Solution. Answer: O, 10 N, 20 N, 38N, 39N, 29N Our 10.0 kg mystery bx rest on a horizontal floor. The coefficent of static friction is µs= 0.40 and the coefficent of kinetic friction is µk= 0.30. Determine the force of friction Ffr acting on the box

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 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

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

Circular Motion and Gravitation Practice Test Provincial Questions

Circular Motion and Gravitation Practice Test Provincial Questions Circular Motion and Gravitation Practice Test Provincial Questions 1. A 1 200 kg car is traveling at 25 m s on a horizontal surface in a circular path of radius 85 m. What is the net force acting on this

More information

PH 2213 : Chapter 05 Homework Solutions

PH 2213 : Chapter 05 Homework Solutions PH 2213 : Chapter 05 Homework Solutions Problem 5.4 : The coefficient of static friction between hard rubber and normal street pavement is about 0.90. On how steep a hill (maximum angle) can you leave

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

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

Study Questions/Problems Week 4

Study Questions/Problems Week 4 Study Questions/Problems Week 4 Chapter 6 treats many topics. I have selected on average less than three problems from each topic. I suggest you do them all. Likewise for the Conceptual Questions and exercises,

More information

HATZIC SECONDARY SCHOOL

HATZIC SECONDARY SCHOOL HATZIC SECONDARY SCHOOL PROVINCIAL EXAMINATION ASSIGNMENT CIRCULAR MOTION MULTIPLE CHOICE / 30 OPEN ENDED / 65 TOTAL / 95 NAME: 1. An object travels along a path at constant speed. There is a constant

More information

1D-04 Radial Acceleration & Tangential Velocity

1D-04 Radial Acceleration & Tangential Velocity 1D-04 Radial Acceleration & Tangential Velocity Once the string is cut, where is the ball going? AT ANY INSTANT, THE VELOCITY VECTOR OF THE BALL IS DIRECTED ALONG THE TANGENT. AT THE INSTANT WHEN THE BLADE

More information

Newton s Laws.

Newton s Laws. Newton s Laws http://mathsforeurope.digibel.be/images Forces and Equilibrium If the net force on a body is zero, it is in equilibrium. dynamic equilibrium: moving relative to us static equilibrium: appears

More information

WS-CH-4 Motion and Force Show all your work and equations used. Isaac Newton ( )

WS-CH-4 Motion and Force Show all your work and equations used. Isaac Newton ( ) AP PHYSICS 1 WS-CH-4 Motion and Force Show all your work and equations used. Isaac Newton (1643-1727) Isaac Newton was the greatest English mathematician of his generation. He laid the foundation for differential

More information

Dynamics Test K/U 28 T/I 16 C 26 A 30

Dynamics Test K/U 28 T/I 16 C 26 A 30 Name: Dynamics Test K/U 28 T/I 16 C 26 A 30 A. True/False Indicate whether the sentence or statement is true or false. 1. The normal force that acts on an object is always equal in magnitude and opposite

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Diagram 1 A) B - A. B) A - B. C) A + B. D) A B.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Diagram 1 A) B - A. B) A - B. C) A + B. D) A B. Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) In the diagram shown, the unknown vector is 1) Diagram 1 A) B - A. B) A - B. C) A + B.

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

Multiple Choice (A) (B) (C) (D)

Multiple Choice (A) (B) (C) (D) Multiple Choice 1. A ball is fastened to a string and is swung in a vertical circle. When the ball is at the highest point of the circle its velocity and acceleration directions are: (A) (B) (C) (D) 2.

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

Circular Motion CENTRIPETAL ACCELERATION. tf-t,

Circular Motion CENTRIPETAL ACCELERATION. tf-t, Circular Motion Ill SECTION OBJECTIVES Solve problems involving centripetal acceleration. Solve problems involving centripetal force. Explain how the apparent existence of an outward force in circular

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

The diagram below shows a block on a horizontal frictionless surface. A 100.-newton force acts on the block at an angle of 30. above the horizontal.

The diagram below shows a block on a horizontal frictionless surface. A 100.-newton force acts on the block at an angle of 30. above the horizontal. Name: 1) 2) 3) Two students are pushing a car. What should be the angle of each student's arms with respect to the flat ground to maximize the horizontal component of the force? A) 90 B) 0 C) 30 D) 45

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

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 Centrifugal Force is Fictitious? F actual = Centripetal Force F fictitious = Centrifugal Force Center FLEEing Centrifugal Force is Fictitious? Center

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

r r Sample Final questions for PS 150

r r Sample Final questions for PS 150 Sample Final questions for PS 150 1) Which of the following is an accurate statement? A) Rotating a vector about an axis passing through the tip of the vector does not change the vector. B) The magnitude

More information

Practice Test for Midterm Exam

Practice Test for Midterm Exam A.P. Physics Practice Test for Midterm Exam Kinematics 1. Which of the following statements are about uniformly accelerated motion? Select two answers. a) If an object s acceleration is constant then it

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 16, 2000 Time: 90 minutes NAME: STUDENT NO.: (Last) Please Print (Given) LECTURE SECTION

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

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

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

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

Name Period Date A) B) C) D)

Name Period Date A) B) C) D) Example Problems 9.2 E1. A car rounds a curve of constant radius at a constant speed. Which diagram best represents the directions of both the car s velocity and acceleration? Explain: A) B) C) D) E2.

More information

Exam #2, Chapters 5-7 PHYS 101-4M MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Exam #2, Chapters 5-7 PHYS 101-4M MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Exam #2, Chapters 5-7 Name PHYS 101-4M MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) The quantity 1/2 mv2 is A) the potential energy of the object.

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

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

Physics 8 Monday, October 12, 2015

Physics 8 Monday, October 12, 2015 Physics 8 Monday, October 12, 2015 HW5 will be due Friday. (HW5 is just Ch9 and Ch10 problems.) You re reading Chapter 12 ( torque ) this week, even though in class we re just finishing Ch10 / starting

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

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

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

Blueberry Muffin Nov. 29/30, 2016 Period: Names: Blueberry Muffin Nov. 29/30, 2016 Period: Names: Congratulations! 1. To solve the problems, use your etextbook, physical textbooks, physics websites, your Sketchbooks. 2. Show your thinking through calculations,

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

In this lecture we will discuss three topics: conservation of energy, friction, and uniform circular motion.

In this lecture we will discuss three topics: conservation of energy, friction, and uniform circular motion. 1 PHYS:100 LECTURE 9 MECHANICS (8) In this lecture we will discuss three topics: conservation of energy, friction, and uniform circular motion. 9 1. Conservation of Energy. Energy is one of the most fundamental

More information

Circular Motion. 2 types of Acceleration. Centripetal Force and Acceleration. In a circle. Constant Velocity vs. Constant Speed.

Circular Motion. 2 types of Acceleration. Centripetal Force and Acceleration. In a circle. Constant Velocity vs. Constant Speed. Circular Motion What does it mean to accelerate Centripetal Force and Acceleration Constant Velocity vs. Constant Speed. 2 types of Acceleration In a circle Direction of acceleration / velocity top view

More information

PSI AP Physics B Circular Motion

PSI AP Physics B Circular Motion PSI AP Physics B Circular Motion Multiple Choice 1. A ball is fastened to a string and is swung in a vertical circle. When the ball is at the highest point of the circle its velocity and acceleration directions

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

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

Chapter 6. Force and Motion-II (Friction, Drag, Circular Motion)

Chapter 6. Force and Motion-II (Friction, Drag, Circular Motion) Chapter 6 Force and Motion-II (Friction, Drag, Circular Motion) 6.2 Frictional Force: Motion of a crate with applied forces There is no attempt at sliding. Thus, no friction and no motion. NO FRICTION

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

Physics 8 Wednesday, October 11, 2017

Physics 8 Wednesday, October 11, 2017 Physics 8 Wednesday, October 11, 2017 HW5 due Friday. It s really Friday this week! Homework study/help sessions (optional): Bill will be in DRL 2C6 Wednesdays from 4 6pm (today). Grace will be in DRL

More information

a reference frame that accelerates in a straight line a reference frame that moves along a circular path Straight Line Accelerated Motion

a reference frame that accelerates in a straight line a reference frame that moves along a circular path Straight Line Accelerated Motion 1.12.1 Introduction Go back to lesson 9 and provide bullet #3 In today s lesson we will consider two examples of non-inertial reference frames: a reference frame that accelerates in a straight line a reference

More information

SPH4U Sample Test Dynamics

SPH4U Sample Test Dynamics 1of14 True/False Indicate whether the sentence or statement is true or false. 1. The normal force that acts on an object is always equal in magnitude and opposite in direction to the gravitational force

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

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

SEE the list given for chapter 04 where Newton s laws were introduced.

SEE the list given for chapter 04 where Newton s laws were introduced. PH2213 : Examples from Chapter 5 : Applying Newton s Laws Key Concepts Newton s Laws (basically Σ F = m a ) allow us to relate the forces acting on an object (left-hand side) to the motion of the object,

More information

66 Chapter 6: FORCE AND MOTION II

66 Chapter 6: FORCE AND MOTION II Chapter 6: FORCE AND MOTION II 1 A brick slides on a horizontal surface Which of the following will increase the magnitude of the frictional force on it? A Putting a second brick on top B Decreasing the

More information

Physics 111: Mechanics Lecture 9

Physics 111: Mechanics Lecture 9 Physics 111: Mechanics Lecture 9 Bin Chen NJIT Physics Department Circular Motion q 3.4 Motion in a Circle q 5.4 Dynamics of Circular Motion If it weren t for the spinning, all the galaxies would collapse

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

Exam 1 Solutions. Kinematics and Newton s laws of motion

Exam 1 Solutions. Kinematics and Newton s laws of motion Exam 1 Solutions Kinematics and Newton s laws of motion No. of Students 80 70 60 50 40 30 20 10 0 PHY231 Spring 2012 Midterm Exam 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Raw Score 1. In which

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 6. Force and Motion-II

Chapter 6. Force and Motion-II Chapter 6 Force and Motion-II 6.2 Friction Frictional Forces Friction has its basis in surfaces that are not completely smooth: Frictional Forces The static frictional force keeps an object from starting

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

Gravity. Gravity and Newton. What really happened? The history of Gravity 3/9/15. Sir Isaac Newton theorized the Law of Gravitation in 1687

Gravity. Gravity and Newton. What really happened? The history of Gravity 3/9/15. Sir Isaac Newton theorized the Law of Gravitation in 1687 3/9/15 Gravity and Newton Gravity What really happened? Probably the more correct version of the story is that Newton, upon observing an apple fall from a tree, began to think along the following lines:

More information

Physics 2211 ABC Quiz #3 Solutions Spring 2017

Physics 2211 ABC Quiz #3 Solutions Spring 2017 Physics 2211 ABC Quiz #3 Solutions Spring 2017 I. (16 points) A block of mass m b is suspended vertically on a ideal cord that then passes through a frictionless hole and is attached to a sphere of mass

More information

PHY131H1F Introduction to Physics I Review of the first half Chapters Error Analysis

PHY131H1F Introduction to Physics I Review of the first half Chapters Error Analysis PHY131H1F Introduction to Physics I Review of the first half Chapters 1-8 + Error Analysis Position, Velocity, Acceleration Significant Figures, Measurements, Errors Equations of constant acceleration

More information

4) Vector = and vector = What is vector = +? A) B) C) D) E)

4) Vector = and vector = What is vector = +? A) B) C) D) E) 1) Suppose that an object is moving with constant nonzero acceleration. Which of the following is an accurate statement concerning its motion? A) In equal times its speed changes by equal amounts. B) In

More information

AP Physics First Nine Weeks Review

AP Physics First Nine Weeks Review AP Physics First Nine Weeks Review 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

PHYSICS 221, FALL 2009 EXAM #1 SOLUTIONS WEDNESDAY, SEPTEMBER 30, 2009

PHYSICS 221, FALL 2009 EXAM #1 SOLUTIONS WEDNESDAY, SEPTEMBER 30, 2009 PHYSICS 221, FALL 2009 EXAM #1 SOLUTIONS WEDNESDAY, SEPTEMBER 30, 2009 Note: The unit vectors in the +x, +y, and +z directions of a right-handed Cartesian coordinate system are î, ĵ, and ˆk, respectively.

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

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

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