Chapter 9. Rotational Dynamics


 Dennis Preston
 1 years ago
 Views:
Transcription
1 Chapter 9 Rotational Dynamics
2 In pure translational motion, all points on an object travel on parallel paths. The most general motion is a combination of translation and rotation.
3 1) Torque Produces angular acceleration F1 F2 If F1 =  F2,! F 1 +! F 2 = m! a CM 0 = m! a CM Object rotates about CM (or fixed axis) ==> CM remains at rest
4 The amount of torque depends on where and in what direction the force is applied, as well as the location of the axis of rotation.
5 φ r DEFINITION OF TORQUE Magnitude of Torque = (Magnitude of the force) x (Lever arm) τ = Frsinφ Direction: The torque is positive when the force tends to produce a counterclockwise rotation about the axis. SI Unit of Torque: newton x meter (N m)
6 i>clicker How to close door? Which force(s) will cause the greatest angular acceleration? A. F 2 B. F 4 C. F 1 D. F 3 E. F 2 and F 3 (tied)
7 i>clicker A workman struggles to keep large stack of boxes on a dolly. The man s right foot is on the axle of the dolly. Assuming that the boxes are identical, which one creates the greatest torque wrt the axle? Line of action lever arm
8 i>clicker A child (mass 25 kg) and his dad (mass 85 kg) stand on opposite ends of seesaw as shown. What is the sign of the net torque? A. + B.  C. The net torque is zero
9 Example In San Francisco a very simple technique is used to turn around a cable car when it reaches the end of its route. The car rolls onto a turntable, which can rotate about a vertical axis through its center. Then, two people push perpendicularly on the car, one at each end, as shown in the drawing. The turntable is rotated onehalf of a revolution to turn the car around. If the length of the car is 9.20 m and each person pushes with a 185N force, what is the magnitude of the net torque applied to the car?
10 Example You are installing a new spark plug in your car, and the manual specifies that it be tightened to a torque that has a magnitude of 45 N m. Using the data in the drawing, determine the magnitude, F, of the force that you must exert on the wrench.
11 2) Rigid objects in equilibrium A rigid body is in equilibrium if it has zero translational acceleration and zero angular acceleration. In equilibrium, the sum of the externally applied forces is zero, and the sum of the externally applied torques is zero. ax = a y = 0 α = 0
12 Reasoning Strategy 1. Select the object to which the equations for equilibrium are to be applied. 2. Draw a freebody diagram that shows all of the external forces acting on the object. 3. Choose a convenient set of x, y axes and resolve all forces into components that lie along these axes. 4. Apply the equations that specify the balance of forces at equilibrium. (Set the net force in the x and y directions equal to zero.) 5. Select a convenient axis of rotation. Set the sum of the torques about this axis equal to zero. 6. Solve the equations for the desired unknown quantities.
13 i>clicker Consider five hockey pucks on frictionless ice. The drawing shows a top view of the pucks and the three forces that act on each one. As shown, the forces have different magnitudes (F, 2F, or 3F), and are applied at different points on the pucks. Only one of the five pucks can be in equilibrium. Which puck is it? A B C D E
14 Example A person exerts a horizontal force of 190 N in the test apparatus shown in the drawing. Find the horizontal force M (magnitude and direction) that his flexor muscle exerts on his forearm.
15 Example A woman whose weight is 530 N is poised at the right end of a diving board with length 3.90 m. The board has negligible weight and is supported by a fulcrum 1.40 m away from the left end. Find the forces that the bolt and the fulcrum exert on the board.
16 3) Torque due to gravity; centreofgravity a) Torque due to discrete point masses m1 m2 axis W1 W2 r2 r1 τ 1 = W 1 r 1 τ 2 = W 2 r 2 τ = τ 1 + τ 2
17 (b) Continuous mass Wi ri τ = ΔW i r i
18 (c) Centreofgravity (definition) The center of gravity of a rigid body is the point at which its weight can be considered to act when the torque due to the weight is being calculated. Wr cg = ΔW i r i r cg = ΔW i r i W
19 (d) Locating the c.g. For 2 discrete masses (extends to any number) τ = Wr cg = W 1 r 1 + W 2 r 2 r cg = W 1 r 1 + W 2 r 2 W 1 + W 2 Uniform gravity W i = m i g r cg = m 1r 1 + m 2 r 2 m 1 + m 2 = r cm For symmetrical objects, cg is at the geometrical centre
20 Example Find the torque of a symmetrical meter stick with a mass of 1 kg about a fulcrum 15 cm from one end.
21 Balancing r cg = W 1 r 1 + W 2 r 2 W 1 + W 2
22 Finding the centre of gravity Image reprinted with permission of John Wiley and Sons, Inc.
23 i>clicker The drawing shows a wine rack for a single bottle of wine that seems to defy common sense as it balances on a tabletop. Where is the centre of gravity of the combined wine rack and bottle of wine located? a) At the neck of the bottle where it passes through the wine rack. b) Directly above the point where the wine rack touches the tabletop. c) At a location to the right of where the wine rack touches the tabletop. Image reprinted with permission of John Wiley and Sons, Inc.
24 Example The drawing shows a person (weight 584 N) doing pushups. Find the normal force exerted by the floor on each hand and each foot, assuming the person holds this position.
25 Example A uniform board is leaning against a smooth vertical wall. The board is at an angle θ above the horizontal ground. The coefficient of static friction between the ground and the lower end of the board is Find the smallest value for the angle θ, such that the lower end of the board does not slide along the ground. i>clicker Which is the correct freebody diagram? A B C D
26 Example A uniform board is leaning against a smooth vertical wall. The board is at an angle θ above the horizontal ground. The coefficient of static friction between the ground and the lower end of the board is Find the smallest value for the angle θ, such that the lower end of the board does not slide along the ground.
27 4) Moment of Inertia; 2nd law for rotation Translation F = ma m resists acceleration Rotation τ = Iα  I resists angular acceleration
28 Moment of inertia of a point object I = mr 2 FT m r F T = ma T rf T = ma T r τ = mr 2 α τ = Iα Moment of inertia of a rigid object I = 2 m i r i
29
30 5) Angular momentum linear momentum: p = mv angular momentum: τ = Iα = I Δω Δt τ = ΔL Δt L = Iω For a point particle on a circular path, L = mvr Units: kg m 2 /s
31 Conservation of angular momentum τ = ΔL Δt If external torque is zero, L is constant. L = Iω I = 2 m i r i If I decreases, angular speed increases.
32 i>clicker A person sits on a stool that easily rotates. As he holds the dumbbells out, torque is applied briefly to cause him to rotate slowly. When he brings the dumbbells close to his body he rotates faster. Why? Bringing the dumbbells inward, A. increases the moment of inertia. B. decreases the moment of inertia. C. increases the angular momentum. D. decreases the angular momentum. Image reprinted with permission of John Wiley and Sons, Inc.
33 Example Satellite in elliptical orbit L = Iω L A = L P I A ω A = I P ω P mv A r A = mv P r P v A = r P r A v P Image reprinted with permission of John Wiley and Sons, Inc.
34 Example C&J In outer space two identical space modules are joined together by a massless cable. These modules are rotating about their center of mass, which is at the center of the cable because the modules are identical (see the drawing). In each module, the cable is connected to a motor, so that the modules can pull each other together. The initial tangential speed of each module is v 0 = 17 m/s. Then they pull together until the distance between them is reduced by a factor of two. Determine the final tangential speed v f for each module. Answer: 34 m/s
35 Example A small kg object moves on a frictionless horizontal table in a circular path of radius 1.00 m The angular speed is 6.28 rad/s. The object is attached to a string of negligible mass that passes through a small hole in the centre of the circle. Someone under the table begins to pull the string downward to make the circle smaller. If the string will tolerate a tension of no more than 105 N, what is the radius of the smallest possible circle on which the object can move?
36 Example A thin rod has a length of 0.25 m and rotates in a circle on a frictionless tabletop. The axis is perpendicular to the length of the rod at one of its ends. The rod has angular velocity of 0.32 rad/s and a moment of inertia of kg m 2. A bug standing on the axis decides to crawl out to the other end of the rod. When the bug ( mass = kg) gets where it s going, what is the angular velocity of the rod? Answer: 0.26 rad/s
Chapter 9. Rotational Dynamics
Chapter 9 Rotational Dynamics In pure translational motion, all points on an object travel on parallel paths. The most general motion is a combination of translation and rotation. 1) Torque Produces angular
More informationChapter 8 continued. Rotational Dynamics
Chapter 8 continued Rotational Dynamics 8.6 The Action of Forces and Torques on Rigid Objects Chapter 8 developed the concepts of angular motion. θ : angles and radian measure for angular variables ω :
More informationChapter 9. Rotational Dynamics
Chapter 9 Rotational Dynamics 9.1 The Action of Forces and Torques on Rigid Objects In pure translational motion, all points on an object travel on parallel paths. The most general motion is a combination
More informationTorque rotational force which causes a change in rotational motion. This force is defined by linear force multiplied by a radius.
Warm up A remotecontrolled car's wheel accelerates at 22.4 rad/s 2. If the wheel begins with an angular speed of 10.8 rad/s, what is the wheel's angular speed after exactly three full turns? AP Physics
More informationRotational Dynamics continued
Chapter 9 Rotational Dynamics continued 9.1 The Action of Forces and Torques on Rigid Objects Chapter 8 developed the concepts of angular motion. θ : angles and radian measure for angular variables ω :
More informationName Date Period PROBLEM SET: ROTATIONAL DYNAMICS
Accelerated Physics Rotational Dynamics Problem Set Page 1 of 5 Name Date Period PROBLEM SET: ROTATIONAL DYNAMICS Directions: Show all work on a separate piece of paper. Box your final answer. Don t forget
More informationChapter 9. Rotational Dynamics
Chapter 9 Rotational Dynamics 9.1 The Action of Forces and Torques on Rigid Objects In pure translational motion, all points on an object travel on parallel paths. The most general motion is a combination
More informationChapter 8 continued. Rotational Dynamics
Chapter 8 continued Rotational Dynamics 8.4 Rotational Work and Energy Work to accelerate a mass rotating it by angle φ F W = F(cosθ)x x = s = rφ = Frφ Fr = τ (torque) = τφ r φ s F to s θ = 0 DEFINITION
More informationChapter 8 continued. Rotational Dynamics
Chapter 8 continued Rotational Dynamics 8.4 Rotational Work and Energy Work to accelerate a mass rotating it by angle φ F W = F(cosθ)x x = rφ = Frφ Fr = τ (torque) = τφ r φ s F to x θ = 0 DEFINITION OF
More informationLecture 14. Rotational dynamics Torque. Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.
Lecture 14 Rotational dynamics Torque Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. Archimedes, 87 1 BC EXAM Tuesday March 6, 018 8:15 PM 9:45 PM Today s Topics:
More informationTable of Contents. Pg. # Momentum & Impulse (Bozemanscience Videos) 1 1/11/16
Table of Contents g. # 1 1/11/16 Momentum & Impulse (Bozemanscience Videos) 2 1/13/16 Conservation of Momentum 3 1/19/16 Elastic and Inelastic Collisions 4 1/19/16 Lab 1 Momentum 5 1/26/16 Rotational Dynamics
More informationAngular Momentum L = I ω
Angular Momentum L = Iω If no NET external Torques act on a system then Angular Momentum is Conserved. Linitial = I ω = L final = Iω Angular Momentum L = Iω Angular Momentum L = I ω A Skater spins with
More informationChapter 9 TORQUE & Rotational Kinematics
Chapter 9 TORQUE & Rotational Kinematics This motionless person is in static equilibrium. The forces acting on him add up to zero. Both forces are vertical in this case. This car is in dynamic equilibrium
More information= o + t = ot + ½ t 2 = o + 2
Chapters 89 Rotational Kinematics and Dynamics Rotational motion Rotational motion refers to the motion of an object or system that spins about an axis. The axis of rotation is the line about which the
More informationCircular Motion, Pt 2: Angular Dynamics. Mr. Velazquez AP/Honors Physics
Circular Motion, Pt 2: Angular Dynamics Mr. Velazquez AP/Honors Physics Formulas: Angular Kinematics (θ must be in radians): s = rθ Arc Length 360 = 2π rads = 1 rev ω = θ t = v t r Angular Velocity α av
More informationChapter 8, Rotational Equilibrium and Rotational Dynamics. 3. If a net torque is applied to an object, that object will experience:
CHAPTER 8 3. If a net torque is applied to an object, that object will experience: a. a constant angular speed b. an angular acceleration c. a constant moment of inertia d. an increasing moment of inertia
More informationPart 1 of 1. (useful for homework)
Chapter 9 Part 1 of 1 Example Problems & Solutions Example Problems & Solutions (useful for homework) 1 1. You are installing a spark plug in your car, and the manual specifies that it be tightened to
More informationCHAPTER 8 TEST REVIEW MARKSCHEME
AP PHYSICS Name: Period: Date: 50 Multiple Choice 45 Single Response 5 MultiResponse Free Response 3 Short Free Response 2 Long Free Response MULTIPLE CHOICE DEVIL PHYSICS BADDEST CLASS ON CAMPUS AP EXAM
More information31 ROTATIONAL KINEMATICS
31 ROTATIONAL KINEMATICS 1. Compare and contrast circular motion and rotation? Address the following Which involves an object and which involves a system? Does an object/system in circular motion have
More informationMechanics II. Which of the following relations among the forces W, k, N, and F must be true?
Mechanics II 1. By applying a force F on a block, a person pulls a block along a rough surface at constant velocity v (see Figure below; directions, but not necessarily magnitudes, are indicated). Which
More informationChapter 9 Rotational Dynamics
Chapter 9 ROTATIONAL DYNAMICS PREVIEW A force acting at a perpendicular distance from a rotation point, such as pushing a doorknob and causing the door to rotate on its hinges, produces a torque. If the
More informationRolling, Torque & Angular Momentum
PHYS 101 Previous Exam Problems CHAPTER 11 Rolling, Torque & Angular Momentum Rolling motion Torque Angular momentum Conservation of angular momentum 1. A uniform hoop (ring) is rolling smoothly from the
More informationChapter 9: Rotational Dynamics Tuesday, September 17, 2013
Chapter 9: Rotational Dynamics Tuesday, September 17, 2013 10:00 PM The fundamental idea of Newtonian dynamics is that "things happen for a reason;" to be more specific, there is no need to explain rest
More informationTest 7 wersja angielska
Test 7 wersja angielska 7.1A One revolution is the same as: A) 1 rad B) 57 rad C) π/2 rad D) π rad E) 2π rad 7.2A. If a wheel turns with constant angular speed then: A) each point on its rim moves with
More informationQ1. For a completely inelastic twobody collision the kinetic energy of the objects after the collision is the same as:
Coordinator: Dr.. Naqvi Monday, January 05, 015 Page: 1 Q1. For a completely inelastic twobody collision the kinetic energy of the objects after the collision is the same as: ) (1/) MV, where M is the
More informationChapter 910 Test Review
Chapter 910 Test Review Chapter Summary 9.2. The Second Condition for Equilibrium Explain torque and the factors on which it depends. Describe the role of torque in rotational mechanics. 10.1. Angular
More informationRolling, Torque, and Angular Momentum
AP Physics C Rolling, Torque, and Angular Momentum Introduction: Rolling: In the last unit we studied the rotation of a rigid body about a fixed axis. We will now extend our study to include cases where
More informationChapter 8. Rotational Equilibrium and Rotational Dynamics. 1. Torque. 2. Torque and Equilibrium. 3. Center of Mass and Center of Gravity
Chapter 8 Rotational Equilibrium and Rotational Dynamics 1. Torque 2. Torque and Equilibrium 3. Center of Mass and Center of Gravity 4. Torque and angular acceleration 5. Rotational Kinetic energy 6. Angular
More informationPHYSICS 149: Lecture 21
PHYSICS 149: Lecture 21 Chapter 8: Torque and Angular Momentum 8.2 Torque 8.4 Equilibrium Revisited 8.8 Angular Momentum Lecture 21 Purdue University, Physics 149 1 Midterm Exam 2 Wednesday, April 6, 6:30
More information Angular momentum.  Equilibrium. Final Exam. During class (13:55 pm) on 6/27, Mon Room: 412 FMH (classroom)
inal Exam During class (13:55 pm) on 6/27, Mon Room: 412 MH (classroom) Bring scientific calculators No smart phone calculators l are allowed. Exam covers everything learned in this course. tomorrow s
More informationPhysics 201 Midterm Exam 3
Physics 201 Midterm Exam 3 Information and Instructions Student ID Number: Section Number: TA Name: Please fill in all the information above. Please write and bubble your Name and Student Id number on
More informationClass XI Chapter 7 System of Particles and Rotational Motion Physics
Page 178 Question 7.1: Give the location of the centre of mass of a (i) sphere, (ii) cylinder, (iii) ring, and (iv) cube, each of uniform mass density. Does the centre of mass of a body necessarily lie
More informationPhysics 111. Tuesday, November 2, Rotational Dynamics Torque Angular Momentum Rotational Kinetic Energy
ics Tuesday, ember 2, 2002 Ch 11: Rotational Dynamics Torque Angular Momentum Rotational Kinetic Energy Announcements Wednesday, 89 pm in NSC 118/119 Sunday, 6:308 pm in CCLIR 468 Announcements This
More informationPSI AP Physics I Rotational Motion
PSI AP Physics I Rotational Motion MultipleChoice questions 1. Which of the following is the unit for angular displacement? A. meters B. seconds C. radians D. radians per second 2. An object moves from
More informationChapter 8. Rotational Kinematics
Chapter 8 Rotational Kinematics 8.3 The Equations of Rotational Kinematics 8.4 Angular Variables and Tangential Variables The relationship between the (tangential) arc length, s, at some radius, r, and
More informationPSI AP Physics I Rotational Motion
PSI AP Physics I Rotational Motion MultipleChoice questions 1. Which of the following is the unit for angular displacement? A. meters B. seconds C. radians D. radians per second 2. An object moves from
More informationAngular Momentum L = I ω
Angular Momentum L = Iω If no NET external Torques act on a system then Angular Momentum is Conserved. Linitial = I ω = L final = Iω Angular Momentum L = Iω Angular Momentum L = I ω A Skater spins with
More informationRotational Dynamics. A wrench floats weightlessly in space. It is subjected to two forces of equal and opposite magnitude: Will the wrench accelerate?
Rotational Dynamics A wrench floats weightlessly in space. It is subjected to two forces of equal and opposite magnitude: Will the wrench accelerate? A. yes B. no C. kind of? Rotational Dynamics 10.13
More informationChapter 10 Practice Test
Chapter 10 Practice Test 1. At t = 0, a wheel rotating about a fixed axis at a constant angular acceleration of 0.40 rad/s 2 has an angular velocity of 1.5 rad/s and an angular position of 2.3 rad. What
More informationChapter 8. Rotational Motion
Chapter 8 Rotational Motion Rotational Work and Energy W = Fs = s = rθ Frθ Consider the work done in rotating a wheel with a tangential force, F, by an angle θ. τ = Fr W =τθ Rotational Work and Energy
More informationAP Physics QUIZ Chapters 10
Name: 1. Torque is the rotational analogue of (A) Kinetic Energy (B) Linear Momentum (C) Acceleration (D) Force (E) Mass A 5kilogram sphere is connected to a 10kilogram sphere by a rigid rod of negligible
More informationChapter 8 Rotational Motion and Equilibrium. 1. Give explanation of torque in own words after doing balancethetorques lab as an inquiry introduction
Chapter 8 Rotational Motion and Equilibrium Name 1. Give explanation of torque in own words after doing balancethetorques lab as an inquiry introduction 1. The distance between a turning axis and the
More informationAP Physics 1 Torque, Rotational Inertia, and Angular Momentum Practice Problems FACT: The center of mass of a system of objects obeys Newton s second law F = Ma cm. Usually the location of the center
More informationChapter 8. Rotational Motion
Chapter 8 Rotational Motion The Action of Forces and Torques on Rigid Objects In pure translational motion, all points on an object travel on parallel paths. The most general motion is a combination of
More informationPhysics 2210 Fall smartphysics Conservation of Angular Momentum 11/20/2015
Physics 2210 Fall 2015 smartphysics 1920 Conservation of Angular Momentum 11/20/2015 Poll 111803 In the two cases shown above identical ladders are leaning against frictionless walls and are not sliding.
More informationWe define angular displacement, θ, and angular velocity, ω. What's a radian?
We define angular displacement, θ, and angular velocity, ω Units: θ = rad ω = rad/s What's a radian? Radian is the ratio between the length of an arc and its radius note: counterclockwise is + clockwise
More informationTutorBreeze.com 7. ROTATIONAL MOTION. 3. If the angular velocity of a spinning body points out of the page, then describe how is the body spinning?
1. rpm is about rad/s. 7. ROTATIONAL MOTION 2. A wheel rotates with constant angular acceleration of π rad/s 2. During the time interval from t 1 to t 2, its angular displacement is π rad. At time t 2
More informationChapter 8 Lecture Notes
Chapter 8 Lecture Notes Physics 2414  Strauss Formulas: v = l / t = r θ / t = rω a T = v / t = r ω / t =rα a C = v 2 /r = ω 2 r ω = ω 0 + αt θ = ω 0 t +(1/2)αt 2 θ = (1/2)(ω 0 +ω)t ω 2 = ω 0 2 +2αθ τ
More informationChapter 8  Rotational Dynamics and Equilibrium REVIEW
Pagpalain ka! (Good luck, in Filipino) Date Chapter 8  Rotational Dynamics and Equilibrium REVIEW TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. 1) When a rigid body
More informationChapter 12 Static Equilibrium
Chapter Static Equilibrium. Analysis Model: Rigid Body in Equilibrium. More on the Center of Gravity. Examples of Rigid Objects in Static Equilibrium CHAPTER : STATIC EQUILIBRIUM AND ELASTICITY.) The Conditions
More information1 MR SAMPLE EXAM 3 FALL 2013
SAMPLE EXAM 3 FALL 013 1. A merrygoround rotates from rest with an angular acceleration of 1.56 rad/s. How long does it take to rotate through the first rev? A) s B) 4 s C) 6 s D) 8 s E) 10 s. A wheel,
More informationAngular Momentum System of Particles Concept Questions
Question 1: Angular Momentum Angular Momentum System of Particles Concept Questions A nonsymmetric body rotates with an angular speed ω about the z axis. Relative to the origin 1. L 0 is constant. 2.
More informationChapter 8. Rotational Equilibrium and Rotational Dynamics
Chapter 8 Rotational Equilibrium and Rotational Dynamics 1 Force vs. Torque Forces cause accelerations Torques cause angular accelerations Force and torque are related 2 Torque The door is free to rotate
More informationΣF = ma Στ = Iα ½mv 2 ½Iω 2. mv Iω
Thur Oct 22 Assign 9 Friday Today: Torques Angular Momentum x θ v ω a α F τ m I Roll without slipping: x = r Δθ v LINEAR = r ω a LINEAR = r α ΣF = ma Στ = Iα ½mv 2 ½Iω 2 I POINT = MR 2 I HOOP = MR 2 I
More informationAP Physics Multiple Choice Practice Torque
AP Physics Multiple Choice Practice Torque 1. A uniform meterstick of mass 0.20 kg is pivoted at the 40 cm mark. Where should one hang a mass of 0.50 kg to balance the stick? (A) 16 cm (B) 36 cm (C) 44
More informationTopic 1: Newtonian Mechanics Energy & Momentum
Work (W) the amount of energy transferred by a force acting through a distance. Scalar but can be positive or negative ΔE = W = F! d = Fdcosθ Units N m or Joules (J) Work, Energy & Power Power (P) the
More informationis the study of and. We study objects. is the study of and. We study objects.
Static Equilibrium Translational Forces Torque Unit 4 Statics Dynamics vs Statics is the study of and. We study objects. is the study of and. We study objects. Recall Newton s First Law All objects remain
More informationIt will be most difficult for the ant to adhere to the wheel as it revolves past which of the four points? A) I B) II C) III D) IV
AP Physics 1 Lesson 16 Homework Newton s First and Second Law of Rotational Motion Outcomes Define rotational inertia, torque, and center of gravity. State and explain Newton s first Law of Motion as it
More informationSlide 1 / 37. Rotational Motion
Slide 1 / 37 Rotational Motion Slide 2 / 37 Angular Quantities An angle θ can be given by: where r is the radius and l is the arc length. This gives θ in radians. There are 360 in a circle or 2π radians.
More informationPHYSICS  CLUTCH 1E CH 12: TORQUE & ROTATIONAL DYNAMICS.
!! www.clutchprep.com INTRO TO TORQUE TORQUE is a twist that a Force gives an object around an axis of rotation.  For example, when you push on a door, it rotates around its hinges.  When a Force acts
More informationPHYSICS  CLUTCH CH 12: TORQUE & ROTATIONAL DYNAMICS.
!! www.clutchprep.com TORQUE & ACCELERATION (ROTATIONAL DYNAMICS) When a Force causes rotation, it produces a Torque. Think of TORQUE as the equivalent of FORCE! FORCE (F) TORQUE (τ)  Causes linear acceleration
More informationAngular Speed and Angular Acceleration Relations between Angular and Linear Quantities
Angular Speed and Angular Acceleration Relations between Angular and Linear Quantities 1. The tires on a new compact car have a diameter of 2.0 ft and are warranted for 60 000 miles. (a) Determine the
More informationFall 2007 RED Barcode Here Physics 105, sections 1 and 2 Please write your CID Colton
Fall 007 RED Barcode Here Physics 105, sections 1 and Exam 3 Please write your CID Colton 3669 3 hour time limit. One 3 5 handwritten note card permitted (both sides). Calculators permitted. No books.
More informationChapter 8 Lecture. Pearson Physics. Rotational Motion and Equilibrium. Prepared by Chris Chiaverina Pearson Education, Inc.
Chapter 8 Lecture Pearson Physics Rotational Motion and Equilibrium Prepared by Chris Chiaverina Chapter Contents Describing Angular Motion Rolling Motion and the Moment of Inertia Torque Static Equilibrium
More informationBig Idea 4: Interactions between systems can result in changes in those systems. Essential Knowledge 4.D.1: Torque, angular velocity, angular
Unit 7: Rotational Motion (angular kinematics, dynamics, momentum & energy) Name: Big Idea 3: The interactions of an object with other objects can be described by forces. Essential Knowledge 3.F.1: Only
More informationChapter 4. Forces and Newton s Laws of Motion. continued
Chapter 4 Forces and Newton s Laws of Motion continued Quiz 3 4.7 The Gravitational Force Newton s Law of Universal Gravitation Every particle in the universe exerts an attractive force on every other
More informationPractice Test 3. Name: Date: ID: A. Multiple Choice Identify the choice that best completes the statement or answers the question.
Name: Date: _ Practice Test 3 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A wheel rotates about a fixed axis with an initial angular velocity of 20
More informationUnit 4 Statics. Static Equilibrium Translational Forces Torque
Unit 4 Statics Static Equilibrium Translational Forces Torque 1 Dynamics vs Statics Dynamics: is the study of forces and motion. We study why objects move. Statics: is the study of forces and NO motion.
More informationPhysics 201, Practice Midterm Exam 3, Fall 2006
Physics 201, Practice Midterm Exam 3, Fall 2006 1. A figure skater is spinning with arms stretched out. A moment later she rapidly brings her arms close to her body, but maintains her dynamic equilibrium.
More informationRotational Dynamics continued
Chapter 9 Rotational Dynamics continued 9.4 Newton s Second Law for Rotational Motion About a Fixed Axis ROTATIONAL ANALOG OF NEWTON S SECOND LAW FOR A RIGID BODY ROTATING ABOUT A FIXED AXIS I = ( mr 2
More informationChapter 8. Rotational Equilibrium and Rotational Dynamics
Chapter 8 Rotational Equilibrium and Rotational Dynamics Wrench Demo Torque Torque, τ, is the tendency of a force to rotate an object about some axis τ = Fd F is the force d is the lever arm (or moment
More informationPractice. Newton s 3 Laws of Motion. Recall. Forces a push or pull acting on an object; a vector quantity measured in Newtons (kg m/s²)
Practice A car starts from rest and travels upwards along a straight road inclined at an angle of 5 from the horizontal. The length of the road is 450 m and the mass of the car is 800 kg. The speed of
More informationWebreview Torque and Rotation Practice Test
Please do not write on test. ID A Webreview  8.2 Torque and Rotation Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A 0.30mradius automobile
More informationRotational Motion What is the difference between translational and rotational motion? Translational motion.
Rotational Motion 1 1. What is the difference between translational and rotational motion? Translational motion Rotational motion 2. What is a rigid object? 3. What is rotational motion? 4. Identify and
More informationQuestion 7.1: Answer. Geometric centre; No
Question 7.1: Give the location of the centre of mass of a (i) sphere, (ii) cylinder, (iii) ring,, and (iv) cube, each of uniform mass density. Does the centre of mass of a body necessarily lie inside
More informationBig Ideas 3 & 5: Circular Motion and Rotation 1 AP Physics 1
Big Ideas 3 & 5: Circular Motion and Rotation 1 AP Physics 1 1. A 50kg boy and a 40kg girl sit on opposite ends of a 3meter seesaw. How far from the girl should the fulcrum be placed in order for the
More informationName: Date: Period: AP Physics C Rotational Motion HO19
1.) A wheel turns with constant acceleration 0.450 rad/s 2. (99) Rotational Motion H19 How much time does it take to reach an angular velocity of 8.00 rad/s, starting from rest? Through how many revolutions
More informationChapter 8. Centripetal Force and The Law of Gravity
Chapter 8 Centripetal Force and The Law of Gravity Centripetal Acceleration An object traveling in a circle, even though it moves with a constant speed, will have an acceleration The centripetal acceleration
More informationRotational Kinetic Energy
Lecture 17, Chapter 10: Rotational Energy and Angular Momentum 1 Rotational Kinetic Energy Consider a rigid body rotating with an angular velocity ω about an axis. Clearly every point in the rigid body
More informationReview PHYS114 Chapters 47
Review PHYS114 Chapters 47 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A 27 kg object is accelerated at a rate of 1.7 m/s 2. What force does
More informationPractice Test 3. Multiple Choice Identify the choice that best completes the statement or answers the question.
Practice Test 3 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A wheel rotates about a fixed axis with an initial angular velocity of 20 rad/s. During
More informationPhysics Fall Mechanics, Thermodynamics, Waves, Fluids. Lecture 20: Rotational Motion. Slide 201
Physics 1501 Fall 2008 Mechanics, Thermodynamics, Waves, Fluids Lecture 20: Rotational Motion Slide 201 Recap: center of mass, linear momentum A composite system behaves as though its mass is concentrated
More informationDynamicsNewton's 2nd Law
1. A constant unbalanced force is applied to an object for a period of time. Which graph best represents the acceleration of the object as a function of elapsed time? 2. The diagram below shows a horizontal
More informationUse the following to answer question 1:
Use the following to answer question 1: On an amusement park ride, passengers are seated in a horizontal circle of radius 7.5 m. The seats begin from rest and are uniformly accelerated for 21 seconds to
More informationEquilibrium & Elasticity
PHYS 101 Previous Exam Problems CHAPTER 12 Equilibrium & Elasticity Static equilibrium Elasticity 1. A uniform steel bar of length 3.0 m and weight 20 N rests on two supports (A and B) at its ends. A block
More informationPhysics 2210 Fall smartphysics Rotational Statics 11/18/2015
Physics 2210 Fall 2015 smartphysics 1718 Rotational Statics 11/18/2015 τ TT = L T 1 sin 150 = 1 T 2 1L Poll 111801 τ TT = L 2 T 2 sin 150 = 1 4 T 2L 150 150 τ gg = L 2 MM sin +90 = 1 2 MMM +90 MM τ
More informationRotational Dynamics, Moment of Inertia and Angular Momentum
Rotational Dynamics, Moment of Inertia and Angular Momentum Now that we have examined rotational kinematics and torque we will look at applying the concepts of angular motion to Newton s first and second
More informationDynamicsNewton's 2nd Law
1. A constant unbalanced force is applied to an object for a period of time. Which graph best represents the acceleration of the object as a function of elapsed time? 2. The diagram below shows a horizontal
More informationPhysics. Chapter 8 Rotational Motion
Physics Chapter 8 Rotational Motion Circular Motion Tangential Speed The linear speed of something moving along a circular path. Symbol is the usual v and units are m/s Rotational Speed Number of revolutions
More informationUniform Circular Motion
Uniform Circular Motion Motion in a circle at constant angular speed. ω: angular velocity (rad/s) Rotation Angle The rotation angle is the ratio of arc length to radius of curvature. For a given angle,
More informationPHYSICS 220. Lecture 15. Textbook Sections Lecture 15 Purdue University, Physics 220 1
PHYSICS 220 Lecture 15 Angular Momentum Textbook Sections 9.3 9.6 Lecture 15 Purdue University, Physics 220 1 Last Lecture Overview Torque = Force that causes rotation τ = F r sin θ Work done by torque
More information6. Find the net torque on the wheel in Figure about the axle through O if a = 10.0 cm and b = 25.0 cm.
1. During a certain period of time, the angular position of a swinging door is described by θ = 5.00 + 10.0t + 2.00t 2, where θ is in radians and t is in seconds. Determine the angular position, angular
More information