Rotational Mechanics  1


 Karin Ross
 2 years ago
 Views:
Transcription
1 Rotational Mechanics  1
2 The Radian The radian is a unit of angular measure. The radian can be defined as the arc length s along a circle divided by the radius r. s r
3 Comparing degrees and radians rad Relating degrees and radians rad rad 180
4 Average Angular Speed The average angular speed, ω, of a rotating rigid object is the ratio of the angular displacement to the time interval av f i t t t f i
5 Instantaneous angular speed is defined as the limit of the average speed as the time interval approaches zero lim t 0 t Units of angular speed are radians/sec (rad/s). Speed is positive if θ is increasing (counterclockwise rotation). Speed is negative if θ is decreasing (clockwise rotation).
6 A particle moves along a circular path of radius R with velocity of constant magnitude u. The time for one rotation is the period, T.
7 Basic Definitions & Units Period T Frequency : time for one rotation f : # of rotations/time interval 1 f If T is in seconds s, f is in s T Angular velocity magnitude : 2 f Unit for angular velocity: radians sec 1 2 T
8 The magnitude of the particle's velocity is the ratio of distance moved in one rotation to the time (period) required for one rotation. u 2 R T
9 The magnitude of the particle's velocity is the ratio of distance moved in one rotation to the time (period) required for one rotation. 2 R u T This can also be expressed in terms of the frequency f : u 2 Rf
10 The magnitude of the particle's velocity is the ratio of distance moved in one rotation to the time (period) required for one rotation. 2 R u T This can also be expressed in terms of the frequency f : u 2 Rf and in terms of the angular velocity u R
11 In time interval t the particle moves along an arc of length s. The magnitude of the particle s velocity is s/ t.
12 The CHANGE in the velocity vector during this time interval is u.
13 The CHANGE in the velocity vector during this time interval is u.
14 The CHANGE in the velocity vector during this time interval is u. The particle moves a horizontal distance x during this time interval.
15 Over a shorter time interval, the length of the arc s approaches the length of the chord x. The velocity CHANGE is u = u 2 + (u 1 )
16 These triangles are similar, i.e., their sides have the same ratio: u x u or u x u R R and as the angle gets smaller s approaches x in length.
17 These triangles are similar, i.e., their sides have the same ratio: u x u or u x u R R and as the angle gets smaller s approaches x in length, so u u s. R
18 The magnitude of the average acceleration is then u u s u u aav u. t R t R R This is the centripetal acceleration of the particle.
19 Centripetal acceleration can be expressed in these equivalent forms: u 2 4 R a c R 4 Rf 2 R T 2 2
20 Average and Instantaneous Angular Acceleration Average angular acceleration a av of an object is defined as the ratio of the change in the angular speed to the time it takes for the object to undergo the change: f i aav t t t f i Instantaneous angular acceleration: a lim t 0 t
21 Relating Linear and Angular Motion If u is constant: If is constant: x ut t
22 Relating Linear and Angular Motion If a is constant: If a is constant: 1 1 x u t at t at i 2 2 i 2 2 i u u at at u u 2a x 2a i s r Tangential velocity: u Tangential acceleration: t r a t ra
23 Total Acceleration The tangential component of the acceleration is due to changing speed. The centripetal component of the acceleration is due to changing direction. Total acceleration can be found from these components 2 2 t c a a a
24 Grasp the axis of rotation with your right hand. Wrap your fingers in the direction of rotation. Your thumb points in the direction of ω. Vector Nature of Angular Quantities Angular displacement, velocity and acceleration are all vector quantities. Direction can be more completely defined by using the right hand rule
25 Angular Velocity Directions, Example In (a), the disk rotates clockwise. The angular velocity is into the page/screen. In (b), the disk rotates counterclockwise. The angular velocity is out of the page/screen.
26 Centripetal Acceleration and Centripetal Force From Newton s second law: F c = ma c Centripetal force, F c, is not an added force. F c can be supplied by a force that maintains an object on a circular path. Examples:  String tension  Gravity  Friction
27 Centripetal Force Example 1 A ball of mass m is attached to a string. Its weight is supported by a frictionless table. The tension in the string causes the ball to move in a circle. The centripetal force is supplied by the string tension: F ma T c c mu r 2
28 Centripetal Force Example 2 Car on a level curve The centripetal force is supplied by the static friction force. mu 2 F f mg C s s r u s gr
29 Centripetal Force Example 3 Car on a banked curve The centripetal force is supplied by the horizontal component of the normal force. 2 mu nsin n cos mg r 2 nsin u tan n cos gr a c gtan
30 Rotational Mechanics Questions
31 A particle rotating in a circle undergoes uniform angular acceleration. Which (one or more) of these graphs could be associated with this kind of motion?
32 A particle rotating in a circle undergoes uniform angular acceleration. Which (one or more) of these graphs could be associated with this kind of motion? A, C
33 A particle rotating in a circle undergoes uniform angular acceleration. Which (one or more) of these graphs could be associated with this kind of motion?
34 A particle rotating in a circle undergoes uniform angular acceleration. Which (one or more) of these graphs could be associated with this kind of motion? A, B, C, E
35 A particle rotating in a circle undergoes uniform angular acceleration. Which (one or more) of these graphs could be associated with this kind of motion?
36 A particle rotating in a circle undergoes uniform angular acceleration. Which (one or more) of these graphs could be associated with this kind of motion? A, B, C, D
37 A disk is rotating at a constant rate about a vertical axis through its center. Point Q is twice as far from the center of the disk as point P is. The angular velocity of Q at a given time is A. twice as big as P's. B. the same as P's. C. half as big as P's. D. none of the above.
38 A disk is rotating at a constant rate about a vertical axis through its center. Point Q is twice as far from the center of the disk as point P is. The angular velocity of Q at a given time is A. twice as big as P's. B. the same as P's. C. half as big as P's. D. none of the above.
39 The figure shows the velocity and acceleration of a particle at a particular instant in three situations In which situation, and at that instant, is the speed increasing?
40 The figure shows the velocity and acceleration of a particle at a particular instant in three situations In which situation, and at that instant, is the speed increasing? B
41 The figure shows the velocity and acceleration of a particle at a particular instant in three situations In which situation, and at that instant, is the speed decreasing?
42 The figure shows the velocity and acceleration of a particle at a particular instant in three situations In which situation, and at that instant, is the speed increasing? C
43 The figure shows the velocity and acceleration of a particle at a particular instant in three situations In which situation, and at that instant, is the speed not changing?
44 The figure shows the velocity and acceleration of a particle at a particular instant in three situations In which situation, and at that instant, is the speed not changing? A (a is centripetal)
45 A particle P moves in a circle in a horizontal plane. The motion is counterclockwise, as viewed from above. If the particle undergoes positive angular acceleration, which drawing correctly represents the net horizontal force (red arrow) applied to the particle?
46 A particle P moves in a circle in a horizontal plane. The motion is counterclockwise, as viewed from above. If the particle undergoes positive angular acceleration, which drawing correctly represents the net horizontal force (red arrow) applied to the particle? C
47 If the particle undergoes positive angular acceleration, which drawing correctly represents the net horizontal force (red arrow) applied to the particle? C (The net force is the vector sum of the tangential and centripetal forces.)
48 If the particle moves with constant angular velocity, which drawing correctly represents the net horizontal force (red arrow) applied to the particle?
49 If the particle moves with constant angular velocity, which drawing correctly represents the net horizontal force (red arrow) applied to the particle? A
50 A nut is located m from the axis of a machine part that rotates uniformly at a rate of 120. times per second. Calculate the period of rotation.
51 A nut is located m from the axis of a machine part that rotates uniformly at a rate of 120. times per second. Calculate the period of rotation. T = (1/120) s
52 A nut is located m from the axis of a machine part that rotates uniformly at a rate of 120. times per second. Calculate the distance the nut moves in 2.00 seconds.
53 A nut is located m from the axis of a machine part that rotates uniformly at a rate of 120. times per second. Calculate the distance the nut moves in 2.00 seconds. 2 r T s t 2 r t T 2.25 m 2 s 120 m 377 m 1120 s
54 Calculate the time required for the nut to move through an angle of π radians.
55 Calculate the time required for the nut to move through an angle of π radians. t 2 T t t T T T 1120 s 1 s
56 7.21 A 55.0kg ice skater is moving at 4.00 m/s when she grabs the loose end of a rope, the opposite end of which is tied to a pole. She then moves in a circle of radius m around the pole.
57 7.21 A 55.0kg ice skater is moving at 4.00 m/s when she grabs the loose end of a rope, the opposite end of which is tied to a pole. She then moves in a circle of radius m around the pole. Write down everything you know:
58 7.21 A 55.0kg ice skater is moving at 4.00 m/s when she grabs the loose end of a rope, the opposite end of which is tied to a pole. She then moves in a circle of radius m around the pole. Write down everything you know: M = 55 kg, u = 4 m/s, R =.8 m
59 7.21 A 55.0kg ice skater is moving at 4.00 m/s when she grabs the loose end of a rope, the opposite end of which is tied to a pole. She then moves in a circle of radius m around the pole. (a) Determine the force exerted by the horizontal rope on her arms.
60 7.21 A 55.0kg ice skater is moving at 4.00 m/s when she grabs the loose end of a rope, the opposite end of which is tied to a pole. She then moves in a circle of radius m around the pole. (a) Determine the force exerted by the horizontal rope on her arms. This force is A. tangent to the circular path. B. directed inward. C. directed outward.
61 7.21 A 55.0kg ice skater is moving at 4.00 m/s when she grabs the loose end of a rope, the opposite end of which is tied to a pole. She then moves in a circle of radius m around the pole. (a) Determine the force exerted by the horizontal rope on her arms. This force is A. tangent to the circular path. B. directed inward (centripetal force). C. directed outward.
62 7.21 A 55.0kg ice skater is moving at 4.00 m/s when she grabs the loose end of a rope, the opposite end of which is tied to a pole. She then moves in a circle of radius m around the pole. (a) Determine the force exerted by the horizontal rope on her arms. F c 2 2 mu 55 kg 4 m s R.8 m 1100 N
63 7.21 A 55.0kg ice skater is moving at 4.00 m/s when she grabs the loose end of a rope, the opposite end of which is tied to a pole. She then moves in a circle of radius m around the pole. (b) Compare this force (1100 N) with her weight.
64 7.21 A 55.0kg ice skater is moving at 4.00 m/s when she grabs the loose end of a rope, the opposite end of which is tied to a pole. She then moves in a circle of radius m around the pole. (b) Compare this force (1100 N) with her weight. F c mg 1100 N 2 55 kg 9.8 m s
65 7.23 A truck can go around a flat curve of radius 150 m with a maximum speed of 32.0 m/s. With what maximum speed can it go around a curve of 75 m?
66 7.23 A truck can go around a flat curve of radius 150 m with a maximum speed of 32.0 m/s. With what maximum speed can it go around a curve of 75 m? The centripetal force is supplied by A. Gravity B. The car s brakes C. Static friction
67 7.23 A truck can go around a flat curve of radius 150 m with a maximum speed of 32.0 m/s. With what maximum speed can it go around a curve of 75 m? The centripetal force is supplied by A. Gravity B. The car s brakes C. Static friction
68 7.23 A truck can go around a flat curve of radius 150 m with a maximum speed of 32.0 m/s. With what maximum speed can it go around a curve of 75 m? R 150 m, 32 m s, R 75 m 1 1 2
69 7.23 A truck can go around a flat curve of radius 150 m with a maximum speed of 32.0 m/s. With what maximum speed can it go around a curve of 75 m? Assumption:
70 7.23 A truck can go around a flat curve of radius 150 m with a maximum speed of 32.0 m/s. With what maximum speed can it go around a curve of 75 m? Assumption: Centripetal force (static friction force) does not change.
71 7.23 A truck can go around a flat curve of radius 150 m with a maximum speed of 32.0 m/s. With what maximum speed can it go around a curve of 75 m? Equate expressions for centripetal acceleration: R 2 R 1 2 R 75 m 32 m s 22.6 m s R1 150 m
72 7.24 A sample of blood is in a centrifuge of radius 15 cm. The mass of a red blood cell is 3.0 x kg and the magnitude of the force acting on it is 4.0 x N. At how many revolutions per second should the centrifuge be operated?
73 7.24 A sample of blood is in a centrifuge of radius 15 cm. The mass of a red blood cell is 3.0 x kg and the magnitude of the force acting on it is 4.0 x N. At how many revolutions per second should the centrifuge be operated? The centripetal force is supplied by A. Gravity B. Friction C. The bottom of the blood sample container.
74 7.24 A sample of blood is in a centrifuge of radius 15 cm. The mass of a red blood cell is 3.0 x kg and the magnitude of the force acting on it is 4.0 x N. At how many revolutions per second should the centrifuge be operated? The centripetal force is supplied by A. Gravity B. Friction C. The bottom of the blood sample container.
75 7.24 A sample of blood is in a centrifuge of radius 15 cm. The mass of a red blood cell is 3.0 x kg and the magnitude of the force acting on it is 4.0 x N. At how many revolutions per second should the centrifuge be operated? Given: R =.15 m, m = 3 x kg, F c = 4 x N
76 7.24 A sample of blood is in a centrifuge of radius 15 cm. The mass of a red blood cell is 3.0 x kg and the magnitude of the force acting on it is 4.0 x N. At how many revolutions per second should the centrifuge be operated? F f c 4 Rf m 2 2 F 11 c 4 10 N Rm 4.15 m 3 10 kg s rev s
Chapter 3.8 & 6 Solutions
Chapter 3.8 & 6 Solutions P3.37. Prepare: We are asked to find period, speed and acceleration. Period and frequency are inverses according to Equation 3.26. To find speed we need to know the distance traveled
More informationUnit 4 Practice Test: Rotational Motion
Unit 4 Practice Test: Rotational Motion Multiple Guess Identify the letter of the choice that best completes the statement or answers the question. 1. How would an angle in radians be converted to an angle
More informationPHY121 #8 Midterm I 3.06.2013
PHY11 #8 Midterm I 3.06.013 AP Physics Newton s Laws AP Exam Multiple Choice Questions #1 #4 1. When the frictionless system shown above is accelerated by an applied force of magnitude F, the tension
More informationChapter 5 Using Newton s Laws: Friction, Circular Motion, Drag Forces. Copyright 2009 Pearson Education, Inc.
Chapter 5 Using Newton s Laws: Friction, Circular Motion, Drag Forces Units of Chapter 5 Applications of Newton s Laws Involving Friction Uniform Circular Motion Kinematics Dynamics of Uniform Circular
More informationPHY231 Section 2, Form A March 22, 2012. 1. Which one of the following statements concerning kinetic energy is true?
1. Which one of the following statements concerning kinetic energy is true? A) Kinetic energy can be measured in watts. B) Kinetic energy is always equal to the potential energy. C) Kinetic energy is always
More informationPHY231 Section 1, Form B March 22, 2012
1. A car enters a horizontal, curved roadbed of radius 50 m. The coefficient of static friction between the tires and the roadbed is 0.20. What is the maximum speed with which the car can safely negotiate
More informationHomework 4. problems: 5.61, 5.67, 6.63, 13.21
Homework 4 problems: 5.6, 5.67, 6.6,. Problem 5.6 An object of mass M is held in place by an applied force F. and a pulley system as shown in the figure. he pulleys are massless and frictionless. Find
More information11. Rotation Translational Motion: Rotational Motion:
11. Rotation Translational Motion: Motion of the center of mass of an object from one position to another. All the motion discussed so far belongs to this category, except uniform circular motion. Rotational
More informationLinear Motion vs. Rotational Motion
Linear Motion vs. Rotational Motion Linear motion involves an object moving from one point to another in a straight line. Rotational motion involves an object rotating about an axis. Examples include a
More informationChapter 10 Rotational Motion. Copyright 2009 Pearson Education, Inc.
Chapter 10 Rotational Motion Angular Quantities Units of Chapter 10 Vector Nature of Angular Quantities Constant Angular Acceleration Torque Rotational Dynamics; Torque and Rotational Inertia Solving Problems
More information3600 s 1 h. 24 h 1 day. 1 day
Week 7 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions of these problems, various details have been changed, so that the answers will come out differently. The method to find the solution
More informationAngular acceleration α
Angular Acceleration Angular acceleration α measures how rapidly the angular velocity is changing: Slide 70 Linear and Circular Motion Compared Slide 7 Linear and Circular Kinematics Compared Slide 7
More informationC B A T 3 T 2 T 1. 1. What is the magnitude of the force T 1? A) 37.5 N B) 75.0 N C) 113 N D) 157 N E) 192 N
Three boxes are connected by massless strings and are resting on a frictionless table. Each box has a mass of 15 kg, and the tension T 1 in the right string is accelerating the boxes to the right at a
More informationAP Physics Circular Motion Practice Test B,B,B,A,D,D,C,B,D,B,E,E,E, 14. 6.6m/s, 0.4 N, 1.5 m, 6.3m/s, 15. 12.9 m/s, 22.9 m/s
AP Physics Circular Motion Practice Test B,B,B,A,D,D,C,B,D,B,E,E,E, 14. 6.6m/s, 0.4 N, 1.5 m, 6.3m/s, 15. 12.9 m/s, 22.9 m/s Answer the multiple choice questions (2 Points Each) on this sheet with capital
More informationCentripetal Force. This result is independent of the size of r. A full circle has 2π rad, and 360 deg = 2π rad.
Centripetal Force 1 Introduction In classical mechanics, the dynamics of a point particle are described by Newton s 2nd law, F = m a, where F is the net force, m is the mass, and a is the acceleration.
More informationVELOCITY, ACCELERATION, FORCE
VELOCITY, ACCELERATION, FORCE velocity Velocity v is a vector, with units of meters per second ( m s ). Velocity indicates the rate of change of the object s position ( r ); i.e., velocity tells you how
More informationTennessee State University
Tennessee State University Dept. of Physics & Mathematics PHYS 2010 CF SU 2009 Name 30% Time is 2 hours. Cheating will give you an Fgrade. Other instructions will be given in the Hall. MULTIPLE CHOICE.
More informationcircular motion & gravitation physics 111N
circular motion & gravitation physics 111N uniform circular motion an object moving around a circle at a constant rate must have an acceleration always perpendicular to the velocity (else the speed would
More information5.2 Rotational Kinematics, Moment of Inertia
5 ANGULAR MOTION 5.2 Rotational Kinematics, Moment of Inertia Name: 5.2 Rotational Kinematics, Moment of Inertia 5.2.1 Rotational Kinematics In (translational) kinematics, we started out with the position
More informationPhysics 2A, Sec B00: Mechanics  Winter 2011 Instructor: B. Grinstein Final Exam
Physics 2A, Sec B00: Mechanics  Winter 2011 Instructor: B. Grinstein Final Exam INSTRUCTIONS: Use a pencil #2 to fill your scantron. Write your code number and bubble it in under "EXAM NUMBER;" an entry
More informationPHYS 1014M, Fall 2005 Exam #3. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
PHYS 1014M, Fall 2005 Exam #3 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A bicycle wheel rotates uniformly through 2.0 revolutions in
More informationPhysics 125 Practice Exam #3 Chapters 67 Professor Siegel
Physics 125 Practice Exam #3 Chapters 67 Professor Siegel Name: Lab Day: 1. A concrete block is pulled 7.0 m across a frictionless surface by means of a rope. The tension in the rope is 40 N; and the
More informationB) 40.8 m C) 19.6 m D) None of the other choices is correct. Answer: B
Practice Test 1 1) Abby throws a ball straight up and times it. She sees that the ball goes by the top of a flagpole after 0.60 s and reaches the level of the top of the pole after a total elapsed time
More informationLecture Presentation Chapter 7 Rotational Motion
Lecture Presentation Chapter 7 Rotational Motion Suggested Videos for Chapter 7 Prelecture Videos Describing Rotational Motion Moment of Inertia and Center of Gravity Newton s Second Law for Rotation Class
More informationF N A) 330 N 0.31 B) 310 N 0.33 C) 250 N 0.27 D) 290 N 0.30 E) 370 N 0.26
Physics 23 Exam 2 Spring 2010 Dr. Alward Page 1 1. A 250N force is directed horizontally as shown to push a 29kg box up an inclined plane at a constant speed. Determine the magnitude of the normal force,
More informationCh 6 Forces. Question: 9 Problems: 3, 5, 13, 23, 29, 31, 37, 41, 45, 47, 55, 79
Ch 6 Forces Question: 9 Problems: 3, 5, 13, 23, 29, 31, 37, 41, 45, 47, 55, 79 Friction When is friction present in ordinary life?  car brakes  driving around a turn  walking  rubbing your hands together
More informationPhysics Notes Class 11 CHAPTER 3 MOTION IN A STRAIGHT LINE
1 P a g e Motion Physics Notes Class 11 CHAPTER 3 MOTION IN A STRAIGHT LINE If an object changes its position with respect to its surroundings with time, then it is called in motion. Rest If an object
More informationEDEXCEL NATIONAL CERTIFICATE/DIPLOMA FURTHER MECHANICAL PRINCIPLES AND APPLICATIONS UNIT 11  NQF LEVEL 3 OUTCOME 3  ROTATING SYSTEMS
EDEXCEL NATIONAL CERTIFICATE/DIPLOMA FURTHER MECHANICAL PRINCIPLES AND APPLICATIONS UNIT 11  NQF LEVEL 3 OUTCOME 3  ROTATING SYSTEMS TUTORIAL 1  ANGULAR MOTION CONTENT Be able to determine the characteristics
More informationPhysics 211 Lecture 4
Physics 211 Lecture 4 Today's Concepts: Newton s Laws a) Acceleration is caused by forces b) Force changes momentum c) Forces always come in pairs d) Good reference frames Mechanics Lecture 4, Slide 1
More informationChapter 4 Dynamics: Newton s Laws of Motion
Chapter 4 Dynamics: Newton s Laws of Motion Units of Chapter 4 Force Newton s First Law of Motion Mass Newton s Second Law of Motion Newton s Third Law of Motion Weight the Force of Gravity; and the NormalForce
More information6: Applications of Newton's Laws
6: Applications of Newton's Laws Friction opposes motion due to surfaces sticking together Kinetic Friction: surfaces are moving relative to each other a.k.a. Sliding Friction Static Friction: surfaces
More informationwww.mathsbox.org.uk Displacement (x) Velocity (v) Acceleration (a) x = f(t) differentiate v = dx Acceleration Velocity (v) Displacement x
Mechanics 2 : Revision Notes 1. Kinematics and variable acceleration Displacement (x) Velocity (v) Acceleration (a) x = f(t) differentiate v = dx differentiate a = dv = d2 x dt dt dt 2 Acceleration Velocity
More informationSolution Derivations for Capa #11
Solution Derivations for Capa #11 1) A horizontal circular platform (M = 128.1 kg, r = 3.11 m) rotates about a frictionless vertical axle. A student (m = 68.3 kg) walks slowly from the rim of the platform
More informationLab 7: Rotational Motion
Lab 7: Rotational Motion Equipment: DataStudio, rotary motion sensor mounted on 80 cm rod and heavy duty bench clamp (PASCO ME9472), string with loop at one end and small white bead at the other end (125
More informationQUESTIONS : CHAPTER5: LAWS OF MOTION
QUESTIONS : CHAPTER5: LAWS OF MOTION 1. What is Aristotle s fallacy? 2. State Aristotlean law of motion 3. Why uniformly moving body comes to rest? 4. What is uniform motion? 5. Who discovered Aristotlean
More informationChapter 24 Physical Pendulum
Chapter 4 Physical Pendulum 4.1 Introduction... 1 4.1.1 Simple Pendulum: Torque Approach... 1 4. Physical Pendulum... 4.3 Worked Examples... 4 Example 4.1 Oscillating Rod... 4 Example 4.3 Torsional Oscillator...
More informationPhysics 1120: Simple Harmonic Motion Solutions
Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Physics 1120: Simple Harmonic Motion Solutions 1. A 1.75 kg particle moves as function of time as follows: x = 4cos(1.33t+π/5) where distance is measured
More informationCHAPTER 28 THE CIRCLE AND ITS PROPERTIES
CHAPTER 8 THE CIRCLE AND ITS PROPERTIES EXERCISE 118 Page 77 1. Calculate the length of the circumference of a circle of radius 7. cm. Circumference, c = r = (7.) = 45.4 cm. If the diameter of a circle
More informationTorque and Rotary Motion
Torque and Rotary Motion Name Partner Introduction Motion in a circle is a straightforward extension of linear motion. According to the textbook, all you have to do is replace displacement, velocity,
More informationPhys222 Winter 2012 Quiz 4 Chapters 2931. Name
Name If you think that no correct answer is provided, give your answer, state your reasoning briefly; append additional sheet of paper if necessary. 1. A particle (q = 5.0 nc, m = 3.0 µg) moves in a region
More informationPhysics 1A Lecture 10C
Physics 1A Lecture 10C "If you neglect to recharge a battery, it dies. And if you run full speed ahead without stopping for water, you lose momentum to finish the race. Oprah Winfrey Static Equilibrium
More informationChapter 13, example problems: x (cm) 10.0
Chapter 13, example problems: (13.04) Reading Fig. 1330 (reproduced on the right): (a) Frequency f = 1/ T = 1/ (16s) = 0.0625 Hz. (since the figure shows that T/2 is 8 s.) (b) The amplitude is 10 cm.
More information11. Describing Angular or Circular Motion
11. Describing Angular or Circular Motion Introduction Examples of angular motion occur frequently. Examples include the rotation of a bicycle tire, a merrygoround, a toy top, a food processor, a laboratory
More informationSOLID MECHANICS TUTORIAL MECHANISMS KINEMATICS  VELOCITY AND ACCELERATION DIAGRAMS
SOLID MECHANICS TUTORIAL MECHANISMS KINEMATICS  VELOCITY AND ACCELERATION DIAGRAMS This work covers elements of the syllabus for the Engineering Council exams C105 Mechanical and Structural Engineering
More informationCHAPTER 6 WORK AND ENERGY
CHAPTER 6 WORK AND ENERGY CONCEPTUAL QUESTIONS. REASONING AND SOLUTION The work done by F in moving the box through a displacement s is W = ( F cos 0 ) s= Fs. The work done by F is W = ( F cos θ). s From
More informationPhysics Honors: Chapter 7 Practice Test
Physics Honors: Chapter 7 Practice Test Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. 1. When an object is moving with uniform circular motion,
More informationChapter 11. h = 5m. = mgh + 1 2 mv 2 + 1 2 Iω 2. E f. = E i. v = 4 3 g(h h) = 4 3 9.8m / s2 (8m 5m) = 6.26m / s. ω = v r = 6.
Chapter 11 11.7 A solid cylinder of radius 10cm and mass 1kg starts from rest and rolls without slipping a distance of 6m down a house roof that is inclined at 30 degrees (a) What is the angular speed
More informationPHYSICS 111 HOMEWORK SOLUTION #10. April 8, 2013
PHYSICS HOMEWORK SOLUTION #0 April 8, 203 0. Find the net torque on the wheel in the figure below about the axle through O, taking a = 6.0 cm and b = 30.0 cm. A torque that s produced by a force can be
More informationNEWTON S LAWS OF MOTION
NEWTON S LAWS OF MOTION Background: Aristotle believed that the natural state of motion for objects on the earth was one of rest. In other words, objects needed a force to be kept in motion. Galileo studied
More informationPhysics 201 Homework 8
Physics 201 Homework 8 Feb 27, 2013 1. A ceiling fan is turned on and a net torque of 1.8 Nm is applied to the blades. 8.2 rad/s 2 The blades have a total moment of inertia of 0.22 kgm 2. What is the
More informationIMPORTANT NOTE ABOUT WEBASSIGN:
Week 8 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions of these problems, various details have been changed, so that the answers will come out differently. The method to find the solution
More informationPhysics 1401  Exam 2 Chapter 5NNew
Physics 1401  Exam 2 Chapter 5NNew 2. The second hand on a watch has a length of 4.50 mm and makes one revolution in 60.00 s. What is the speed of the end of the second hand as it moves in uniform circular
More information226 Chapter 15: OSCILLATIONS
Chapter 15: OSCILLATIONS 1. In simple harmonic motion, the restoring force must be proportional to the: A. amplitude B. frequency C. velocity D. displacement E. displacement squared 2. An oscillatory motion
More informationPHYS 211 FINAL FALL 2004 Form A
1. Two boys with masses of 40 kg and 60 kg are holding onto either end of a 10 m long massless pole which is initially at rest and floating in still water. They pull themselves along the pole toward each
More informationENGINEERING COUNCIL DYNAMICS OF MECHANICAL SYSTEMS D225 TUTORIAL 1 LINEAR AND ANGULAR DISPLACEMENT, VELOCITY AND ACCELERATION
ENGINEERING COUNCIL DYNAMICS OF MECHANICAL SYSTEMS D225 TUTORIAL 1 LINEAR AND ANGULAR DISPLACEMENT, VELOCITY AND ACCELERATION This tutorial covers prerequisite material and should be skipped if you are
More informationE X P E R I M E N T 8
E X P E R I M E N T 8 Torque, Equilibrium & Center of Gravity Produced by the Physics Staff at Collin College Copyright Collin College Physics Department. All Rights Reserved. University Physics, Exp 8:
More information1. Units of a magnetic field might be: A. C m/s B. C s/m C. C/kg D. kg/c s E. N/C m ans: D
Chapter 28: MAGNETIC FIELDS 1 Units of a magnetic field might be: A C m/s B C s/m C C/kg D kg/c s E N/C m 2 In the formula F = q v B: A F must be perpendicular to v but not necessarily to B B F must be
More informationPHYSICS 111 HOMEWORK SOLUTION #10. April 10, 2013
PHYSICS 111 HOMEWORK SOLUTION #10 April 10, 013 0.1 Given M = 4 i + j 3 k and N = i j 5 k, calculate the vector product M N. By simply following the rules of the cross product: i i = j j = k k = 0 i j
More informationOUTCOME 2 KINEMATICS AND DYNAMICS TUTORIAL 2 PLANE MECHANISMS. You should judge your progress by completing the self assessment exercises.
Unit 60: Dynamics of Machines Unit code: H/601/1411 QCF Level:4 Credit value:15 OUTCOME 2 KINEMATICS AND DYNAMICS TUTORIAL 2 PLANE MECHANISMS 2 Be able to determine the kinetic and dynamic parameters of
More informationChapter 6 Circular Motion
Chapter 6 Circular Motion 6.1 Introduction... 1 6.2 Cylindrical Coordinate System... 2 6.2.1 Unit Vectors... 3 6.2.2 Infinitesimal Line, Area, and Volume Elements in Cylindrical Coordinates... 4 Example
More informationLecture 16. Newton s Second Law for Rotation. Moment of Inertia. Angular momentum. Cutnell+Johnson: 9.4, 9.6
Lecture 16 Newton s Second Law for Rotation Moment of Inertia Angular momentum Cutnell+Johnson: 9.4, 9.6 Newton s Second Law for Rotation Newton s second law says how a net force causes an acceleration.
More informationProblem Set 1. Ans: a = 1.74 m/s 2, t = 4.80 s
Problem Set 1 1.1 A bicyclist starts from rest and after traveling along a straight path a distance of 20 m reaches a speed of 30 km/h. Determine her constant acceleration. How long does it take her to
More informationChapter 4. Forces and Newton s Laws of Motion. continued
Chapter 4 Forces and Newton s Laws of Motion continued 4.9 Static and Kinetic Frictional Forces When an object is in contact with a surface forces can act on the objects. The component of this force acting
More information7. Kinetic Energy and Work
Kinetic Energy: 7. Kinetic Energy and Work The kinetic energy of a moving object: k = 1 2 mv 2 Kinetic energy is proportional to the square of the velocity. If the velocity of an object doubles, the kinetic
More informationCurso20122013 Física Básica Experimental I Cuestiones Tema IV. Trabajo y energía.
1. A body of mass m slides a distance d along a horizontal surface. How much work is done by gravity? A) mgd B) zero C) mgd D) One cannot tell from the given information. E) None of these is correct. 2.
More informationPHYSICS 111 HOMEWORK SOLUTION, week 4, chapter 5, sec 17. February 13, 2013
PHYSICS 111 HOMEWORK SOLUTION, week 4, chapter 5, sec 17 February 13, 2013 0.1 A 2.00kg object undergoes an acceleration given by a = (6.00î + 4.00ĵ)m/s 2 a) Find the resultatnt force acting on the object
More informationBHS Freshman Physics Review. Chapter 2 Linear Motion Physics is the oldest science (astronomy) and the foundation for every other science.
BHS Freshman Physics Review Chapter 2 Linear Motion Physics is the oldest science (astronomy) and the foundation for every other science. Galileo (15641642): 1 st true scientist and 1 st person to use
More informationDownloaded from www.studiestoday.com
Class XI Physics Ch. 4: Motion in a Plane NCERT Solutions Page 85 Question 4.1: State, for each of the following physical quantities, if it is a scalar or a vector: Volume, mass, speed, acceleration, density,
More informationANALYTICAL METHODS FOR ENGINEERS
UNIT 1: Unit code: QCF Level: 4 Credit value: 15 ANALYTICAL METHODS FOR ENGINEERS A/601/1401 OUTCOME  TRIGONOMETRIC METHODS TUTORIAL 1 SINUSOIDAL FUNCTION Be able to analyse and model engineering situations
More information1.10 Using Figure 1.6, verify that equation (1.10) satisfies the initial velocity condition. t + ") # x (t) = A! n. t + ") # v(0) = A!
1.1 Using Figure 1.6, verify that equation (1.1) satisfies the initial velocity condition. Solution: Following the lead given in Example 1.1., write down the general expression of the velocity by differentiating
More informationSection 10.7 Parametric Equations
299 Section 10.7 Parametric Equations Objective 1: Defining and Graphing Parametric Equations. Recall when we defined the x (rcos(θ), rsin(θ)) and ycoordinates on a circle of radius r as a function of
More informationCHAPTER 15 FORCE, MASS AND ACCELERATION
CHAPTER 5 FORCE, MASS AND ACCELERATION EXERCISE 83, Page 9. A car initially at rest accelerates uniformly to a speed of 55 km/h in 4 s. Determine the accelerating force required if the mass of the car
More informationPHYSICS 111 HOMEWORK SOLUTION #9. April 5, 2013
PHYSICS 111 HOMEWORK SOLUTION #9 April 5, 2013 0.1 A potter s wheel moves uniformly from rest to an angular speed of 0.16 rev/s in 33 s. Find its angular acceleration in radians per second per second.
More informationChapter 8: Rotational Motion of Solid Objects
Chapter 8: Rotational Motion of Solid Objects 1. An isolated object is initially spinning at a constant speed. Then, although no external forces act upon it, its rotational speed increases. This must be
More informationPhysics: Principles and Applications, 6e Giancoli Chapter 2 Describing Motion: Kinematics in One Dimension
Physics: Principles and Applications, 6e Giancoli Chapter 2 Describing Motion: Kinematics in One Dimension Conceptual Questions 1) Suppose that an object travels from one point in space to another. Make
More informationPhysics 41 HW Set 1 Chapter 15
Physics 4 HW Set Chapter 5 Serway 8 th OC:, 4, 7 CQ: 4, 8 P: 4, 5, 8, 8, 0, 9,, 4, 9, 4, 5, 5 Discussion Problems:, 57, 59, 67, 74 OC CQ P: 4, 5, 8, 8, 0, 9,, 4, 9, 4, 5, 5 Discussion Problems:, 57, 59,
More informationGround Rules. PC1221 Fundamentals of Physics I. Kinematics. Position. Lectures 3 and 4 Motion in One Dimension. Dr Tay Seng Chuan
Ground Rules PC11 Fundamentals of Physics I Lectures 3 and 4 Motion in One Dimension Dr Tay Seng Chuan 1 Switch off your handphone and pager Switch off your laptop computer and keep it No talking while
More informationExam 3 Review Questions PHY Exam 3
Exam 3 Review Questions PHY 2425  Exam 3 Section: 8 1 Topic: Conservation of Linear Momentum Type: Numerical 1 An automobile of mass 1300 kg has an initial velocity of 7.20 m/s toward the north and a
More informationSample Questions for the AP Physics 1 Exam
Sample Questions for the AP Physics 1 Exam Sample Questions for the AP Physics 1 Exam Multiplechoice Questions Note: To simplify calculations, you may use g 5 10 m/s 2 in all problems. Directions: Each
More informationState Newton's second law of motion for a particle, defining carefully each term used.
5 Question 1. [Marks 20] An unmarked police car P is, travelling at the legal speed limit, v P, on a straight section of highway. At time t = 0, the police car is overtaken by a car C, which is speeding
More informationB) 286 m C) 325 m D) 367 m Answer: B
Practice Midterm 1 1) When a parachutist jumps from an airplane, he eventually reaches a constant speed, called the terminal velocity. This means that A) the acceleration is equal to g. B) the force of
More informationChapter 11 Equilibrium
11.1 The First Condition of Equilibrium The first condition of equilibrium deals with the forces that cause possible translations of a body. The simplest way to define the translational equilibrium of
More informationMagnetism. d. gives the direction of the force on a charge moving in a magnetic field. b. results in negative charges moving. clockwise.
Magnetism 1. An electron which moves with a speed of 3.0 10 4 m/s parallel to a uniform magnetic field of 0.40 T experiences a force of what magnitude? (e = 1.6 10 19 C) a. 4.8 10 14 N c. 2.2 10 24 N b.
More informationMechanical Principles
Unit 4: Mechanical Principles Unit code: F/601/1450 QCF level: 5 Credit value: 15 OUTCOME 4 POWER TRANSMISSION TUTORIAL 2 BALANCING 4. Dynamics of rotating systems Single and multilink mechanisms: slider
More informationv v ax v a x a v a v = = = Since F = ma, it follows that a = F/m. The mass of the arrow is unchanged, and ( )
Week 3 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions of these problems, various details have been changed, so that the answers will come out differently. The method to find the solution
More informationSolution: (a) For a positively charged particle, the direction of the force is that predicted by the right hand rule. These are:
Problem 1. (a) Find the direction of the force on a proton (a positively charged particle) moving through the magnetic fields as shown in the figure. (b) Repeat part (a), assuming the moving particle is
More informationMechanics 2. Revision Notes
Mechanics 2 Revision Notes November 2012 Contents 1 Kinematics 3 Constant acceleration in a vertical plane... 3 Variable acceleration... 5 Using vectors... 6 2 Centres of mass 8 Centre of mass of n particles...
More informationTHE NOT SO SIMPLE PENDULUM
INTRODUCTION: THE NOT SO SIMPLE PENDULUM This laboratory experiment is used to study a wide range of topics in mechanics like velocity, acceleration, forces and their components, the gravitational force,
More informationVectors; 2D Motion. Part I. Multiple Choice. 1. v
This test covers vectors using both polar coordinates and ij notation, radial and tangential acceleration, and twodimensional motion including projectiles. Part I. Multiple Choice 1. v h x In a lab experiment,
More informationHalliday, Resnick & Walker Chapter 13. Gravitation. Physics 1A PHYS1121 Professor Michael Burton
Halliday, Resnick & Walker Chapter 13 Gravitation Physics 1A PHYS1121 Professor Michael Burton II_A2: Planetary Orbits in the Solar System + Galaxy Interactions (You Tube) 21 seconds 131 Newton's Law
More informationRotational inertia (moment of inertia)
Rotational inertia (moment of inertia) Define rotational inertia (moment of inertia) to be I = Σ m i r i 2 or r i : the perpendicular distance between m i and the given rotation axis m 1 m 2 x 1 x 2 Moment
More informationHW Set VI page 1 of 9 PHYSICS 1401 (1) homework solutions
HW Set VI page 1 of 9 1030 A 10 g bullet moving directly upward at 1000 m/s strikes and passes through the center of mass of a 5.0 kg block initially at rest (Fig. 1033 ). The bullet emerges from the
More informationThis week s homework. 2 parts Quiz on Friday, Ch. 4 Today s class: Newton s third law Friction Pulleys tension. PHYS 2: Chap.
This week s homework. 2 parts Quiz on Friday, Ch. 4 Today s class: Newton s third law Friction Pulleys tension PHYS 2: Chap. 19, Pg 2 1 New Topic Phys 1021 Ch 7, p 3 A 2.0 kg wood box slides down a vertical
More informationPhysics: Principles and Applications, 6e Giancoli Chapter 4 Dynamics: Newton's Laws of Motion
Physics: Principles and Applications, 6e Giancoli Chapter 4 Dynamics: Newton's Laws of Motion Conceptual Questions 1) Which of Newton's laws best explains why motorists should buckleup? A) the first law
More informationSupplemental Questions
Supplemental Questions The fastest of all fishes is the sailfish. If a sailfish accelerates at a rate of 14 (km/hr)/sec [fwd] for 4.7 s from its initial velocity of 42 km/h [fwd], what is its final velocity?
More informationChapter 13. Gravitation
Chapter 13 Gravitation 13.2 Newton s Law of Gravitation In vector notation: Here m 1 and m 2 are the masses of the particles, r is the distance between them, and G is the gravitational constant. G = 6.67
More informationVectors and Phasors. A supplement for students taking BTEC National, Unit 5, Electrical and Electronic Principles. Owen Bishop
Vectors and phasors Vectors and Phasors A supplement for students taking BTEC National, Unit 5, Electrical and Electronic Principles Owen Bishop Copyrught 2007, Owen Bishop 1 page 1 Electronics Circuits
More informationNo Brain Too Small PHYSICS. 2 kg
MECHANICS: ANGULAR MECHANICS QUESTIONS ROTATIONAL MOTION (2014;1) Universal gravitational constant = 6.67 10 11 N m 2 kg 2 (a) The radius of the Sun is 6.96 10 8 m. The equator of the Sun rotates at a
More informationSOLID MECHANICS BALANCING TUTORIAL BALANCING OF ROTATING BODIES
SOLID MECHANICS BALANCING TUTORIAL BALANCING OF ROTATING BODIES This work covers elements of the syllabus for the Edexcel module 21722P HNC/D Mechanical Principles OUTCOME 4. On completion of this tutorial
More information