Physics 201, Lecture 21
|
|
- Virginia Hancock
- 5 years ago
- Views:
Transcription
1 Physics 201, Lecture 21 Today s Topics q Static Equilibrium of Rigid Objects(Ch ) Review: Rotational and Translational Motion Conditions for Translational and Rotational Equilibrium Demos and Exercises q Stable and Instable Equilibrium (Section 7.9) Hope you have previewed!
2 Review: Torque τ = r F q τ Fsinφ r ( ) Torque depends on F, r, and sinφ No torque If F=0, or φ=0 o /180 o, or r = 0 q The torque acting on the object is proportional to its angular acceleration Στ = I α Moment if inertia
3 Review: Rotational Dynamics Στ = I α Rotational Dynamics compared to 1-D Dynamics Angular Linear τ F α = a = I m ω = ω 0 + αt v v + at θ = θ + ω ω0t 2 αt ω 2 + αδθ 0 = 2 = 0 x = x + v v0t 2 at 2 = v + 2aΔx 0 KE = 1 2 Iω 2 L = I ω KE = 1 2 mv2 p = m v
4 Review: Motion of Rigid Object: Translation + Rotation = +
5 Review: Dynamics For Rigid Objects q Translational Motion Σ F external = M a CM q Rotational Motion Σ τ = dl /dt (= Iα for object around fixed axis)
6 Mechanical Equilibrium (Static)
7 q Mechanic Equilibrium: Mechanic Equilibrium Translational acceleration a=0, AND Rotational acceleration α=0 q Conditions of Mechanic Equilibrium: Ø a=0 The net external force must be zero (think a=f/m) Σ F = 0 Ø α=0 The net external torque must be zero (think α = τ/i) Σ τ = 0 F x =0 F y =0, F Z =0 q Static and Dynamic Equilibrium Note in equilibrium, translational velocity does not have to be 0 Static equilibrium: v=0 Dynamic equilibrium: v =constant (!=0)
8 Mechanical Equilibrium (Case Analyses) N mg mg N center of gravity for board+bottle N m 1 g m 2 g Mg
9 Solving Equilibrium Problems q Draw Free Body Diagram (FBD) with exact acting point of each force q Establish convenient coordinate axes for each object. Ø Apply the First Condition of Equilibrium F net = 0. (Note in 2D this gives you F net,x = 0 and F net,y = 0) q Choose a convenient rotational axis for calculating net torque on object. and then apply τ net = 0. v Note: In the situation of static equilibrium, the choice of rotational axis is arbitrary. Just choose a convenient one such as a pivot (some choices are better, choose a simple one cleverly.) q Solve the resulting simultaneous equations for all of the unknowns.
10 The Acting point of Gravity: Center of Gravity q The force of gravity acting on an object must be considered in determining equilibrium q In finding the torque produced by the force of gravity, all of the weight of the object can be considered to be concentrated at one point called center of gravity (cg) q Effectively, assuming gravitation field is uniform, the CG of an object is the same as its CM (that is usually true at the Phy103 level) x cg = Σm ix i Σm i and y cg = Σm iy i Σm i See demo: finding CG
11 Example of a Free Body Diagram Fig 8.12, p.228 Slide 17 Important: The direction and acting point of each force must be drawn correctly.
12 Another Example of FBD
13 Exercise: Seesaw q Masses of father and daughter are m f =70 kg and m d =45 kg, respectively. The seesaw bar has a mass of M=50 kg. Ø where the father has to sit to balance the bar? Solution: Identify 4 forces as in FBD. Choose the pivot point as origin for torque τ daughter = - m d g L τ seesaw = Mg x 0m =0 τ N = N x 0m =0 τ father = m f g d Στ =0 d= (m d /m f )L = 1.3m Ø How much is N? ΣF=0 N= m f g+m d g+mg = ( )g =1617 N N L= 2m
14 Exercise: Leaning On the Wall (I) q A ladder of mass m=1kg is leaning without slipping on the wall at an angle φ=60 o as shown. Assume there is no friction on the wall. Ø What is the friction from ground. A: 2.8N, B:4.9N, C:9.8N, D: not sure as length is not given Solution: Identify forces (N F,N W, mg, F friction ), draw FBD Take P as the origin for torque. τ NW = N W sinφ L out of page τ mg =- mgsin(90 o -φ)l/2 into page τ NF = τ friction =0 Στ=0 N W sinφ L mgcosφl/2=0 N W =mg/(2tanφ) = 2.83N also: 0= ΣF x = F friction -N W F friction = N W = 2.83 N to the right
15 Exercise: Leaning On the Wall(2) q A ladder of mass m=1kg is leaning without slipping on the wall at an angle φ=60 o as shown. Assume there is no friction on the wall. Ø What is the friction from ground. Solution: Identify forces (N F,N W, mg, F friction ), draw FBD Take CM of the ladder as the origin for torque. (Spend 1-2 min. now, more after class) Repeat steps on previous slide And verify that you get the same answer
16 Exercise: Leaning On the Wall (3) q A ladder of mass m=1kg is leaning without slipping on the wall at an angle φ as shown. There is no friction on the wall and the µ s between the ladder and the ground is Ø What is the minimum angle φ such that ladder does not sliding down? Solution: Identify forces (N F,N W, mg, F friction ), draw FBD Take P as the origin for torque. τ NW = N W sinφ L out of page τ mg =- mgsin(90 o -φ)l/2 into page τ NF = τ friction =0 Στ=0 N W sinφ L mgcosφl/2=0 N W =mg/(2tanφ) also: in y: N F -mg=0 N F =mg in x 0= ΣF x = F friction -N W F friction = N W = mg/(2tanφ) < µ s N F tanφ > 1/(2µ s ) f > 55 o
17 Stable and Unstable Equilibriums (Section. 7.9, conceptual only) q It can be shown that when a system is in equilibrium, the first derivative of its potential energy must be zero. (du/dx=0) This is consistent with conditions F=0, and τ=0 q There are 2 class of equilibrium: Stable and Unstable du/dx=0 and d 2 U/dx 2 >0 du/dx=0 but d 2 U/dx 2 <0 stable equilibrium at x=0 (lowest energy principle) unstable equilibrium at x=0
α = p = m v L = I ω Review: Torque Physics 201, Lecture 21 Review: Rotational Dynamics a = Στ = I α
Physics 1, Lecture 1 Today s Topics q Static Equilibrium of Rigid Objects(Ch. 1.1-3) Review: Rotational and Translational Motion Conditions for Translational and Rotational Equilibrium Demos and Exercises
More informationPhysics 201, Lecture 18
q q Physics 01, Lecture 18 Rotational Dynamics Torque Exercises and Applications Rolling Motion Today s Topics Review Angular Velocity And Angular Acceleration q Angular Velocity (ω) describes how fast
More informationPhysics 101 Lecture 12 Equilibrium
Physics 101 Lecture 12 Equilibrium Assist. Prof. Dr. Ali ÖVGÜN EMU Physics Department www.aovgun.com Static Equilibrium q Equilibrium and static equilibrium q Static equilibrium conditions n Net eternal
More informationPhysics 201, Review 3
Physics 0, Reiew Important Notes: This reiew does not replace your own preparation efforts Exercises used in this reiew do not form a test problem pool. Please practice more with end of chapter problems.
More informationKinematics (special case) Dynamics gravity, tension, elastic, normal, friction. Energy: kinetic, potential gravity, spring + work (friction)
Kinematics (special case) a = constant 1D motion 2D projectile Uniform circular Dynamics gravity, tension, elastic, normal, friction Motion with a = constant Newton s Laws F = m a F 12 = F 21 Time & Position
More informationPhysics 101 Lecture 12 Equilibrium and Angular Momentum
Physics 101 Lecture 1 Equilibrium and Angular Momentum Ali ÖVGÜN EMU Physics Department www.aovgun.com Static Equilibrium q Equilibrium and static equilibrium q Static equilibrium conditions n Net external
More informationGeneral Physics (PHY 2130)
General Physics (PHY 130) Lecture 0 Rotational dynamics equilibrium nd Newton s Law for rotational motion rolling Exam II review http://www.physics.wayne.edu/~apetrov/phy130/ Lightning Review Last lecture:
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 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 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 informationChapter 8. Rotational Equilibrium and Rotational Dynamics
Chapter 8 Rotational Equilibrium and Rotational Dynamics Force vs. Torque Forces cause accelerations Torques cause angular accelerations Force and torque are related Torque The door is free to rotate about
More informationReview for 3 rd Midterm
Review for 3 rd Midterm Midterm is on 4/19 at 7:30pm in the same rooms as before You are allowed one double sided sheet of paper with any handwritten notes you like. The moment-of-inertia about the center-of-mass
More informationStatic Equilibrium; Torque
Static Equilibrium; Torque The Conditions for Equilibrium An object with forces acting on it, but that is not moving, is said to be in equilibrium. The first condition for equilibrium is that the net force
More informationPHY131H1S - Class 20. Pre-class reading quiz on Chapter 12
PHY131H1S - Class 20 Today: Gravitational Torque Rotational Kinetic Energy Rolling without Slipping Equilibrium with Rotation Rotation Vectors Angular Momentum Pre-class reading quiz on Chapter 12 1 Last
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 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 informationPhysics 201. Professor P. Q. Hung. 311B, Physics Building. Physics 201 p. 1/1
Physics 201 p. 1/1 Physics 201 Professor P. Q. Hung 311B, Physics Building Physics 201 p. 2/1 Rotational Kinematics and Energy Rotational Kinetic Energy, Moment of Inertia All elements inside the rigid
More informationAnnouncements Oct 16, 2014
Announcements Oct 16, 2014 1. Prayer 2. While waiting, see how many of these blanks you can fill out: Centripetal Accel.: Causes change in It points but not Magnitude: a c = How to use with N2: Always
More informationDynamics of Rotational Motion
Chapter 10 Dynamics of Rotational Motion To understand the concept of torque. To relate angular acceleration and torque. To work and power in rotational motion. To understand angular momentum. To understand
More informationPLANAR KINETIC EQUATIONS OF MOTION (Section 17.2)
PLANAR KINETIC EQUATIONS OF MOTION (Section 17.2) We will limit our study of planar kinetics to rigid bodies that are symmetric with respect to a fixed reference plane. As discussed in Chapter 16, when
More informationPhysics 101 Lecture 11 Torque
Physics 101 Lecture 11 Torque Dr. Ali ÖVGÜN EMU Physics Department www.aovgun.com Force vs. Torque q Forces cause accelerations q What cause angular accelerations? q A door is free to rotate about an axis
More informationApplication of Forces. Chapter Eight. Torque. Force vs. Torque. Torque, cont. Direction of Torque 4/7/2015
Raymond A. Serway Chris Vuille Chapter Eight Rotational Equilibrium and Rotational Dynamics Application of Forces The point of application of a force is important This was ignored in treating objects as
More informationChapter 12. Static Equilibrium and Elasticity
Chapter 12 Static Equilibrium and Elasticity Static Equilibrium Equilibrium implies that the object moves with both constant velocity and constant angular velocity relative to an observer in an inertial
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 informationPLANAR KINETIC EQUATIONS OF MOTION: TRANSLATION (Sections ) Today s Objectives: Students will be able to: a) Apply the three equations of
PLANAR KINETIC EQUATIONS OF MOTION: TRANSLATION (Sections 17.2-17.3) Today s Objectives: Students will be able to: a) Apply the three equations of motion for a rigid body in planar motion. b) Analyze problems
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 informationReview: Angular Momentum. Physics 201, Lecture 20
q Physics 01, Lecture 0 Today s Topics More on Angular Momentum and Conservation of Angular Momentum Demos and Exercises q Elasticity (Section 1.4. ) Deformation Elastic Modulus (Young s, Shear, Bulk)
More informationPLANAR KINETIC EQUATIONS OF MOTION: TRANSLATION
PLANAR KINETIC EQUATIONS OF MOTION: TRANSLATION Today s Objectives: Students will be able to: 1. Apply the three equations of motion for a rigid body in planar motion. 2. Analyze problems involving translational
More informationAP Pd 3 Rotational Dynamics.notebook. May 08, 2014
1 Rotational Dynamics Why do objects spin? Objects can travel in different ways: Translation all points on the body travel in parallel paths Rotation all points on the body move around a fixed point An
More informationMidterm 3 Thursday April 13th
Welcome back to Physics 215 Today s agenda: Angular momentum Rolling without slipping Midterm Review Physics 215 Spring 2017 Lecture 12-2 1 Midterm 3 Thursday April 13th Material covered: Ch 9 Ch 12 Lectures
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 informationChapter 8 Rotational Equilibrium and Rotational Dynamics Force vs. Torque Forces cause accelerations Torques cause angular accelerations Force and
Chapter 8 Rotational Equilibrium and Rotational Dynamics Force vs. Torque Forces cause accelerations Torques cause angular accelerations Force and torque are related Torque The door is free to rotate about
More informationPhysics 5A Final Review Solutions
Physics A Final Review Solutions Eric Reichwein Department of Physics University of California, Santa Cruz November 6, 0. A stone is dropped into the water from a tower 44.m above the ground. Another stone
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 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 informationChapter 12: Rotation of Rigid Bodies. Center of Mass Moment of Inertia Torque Angular Momentum Rolling Statics
Chapter 1: Rotation of Rigid Bodies Center of Mass Moment of Inertia Torque Angular Momentum Rolling Statics Translational vs Rotational / / 1/ m x v dx dt a dv dt F ma p mv KE mv Work Fd P Fv / / 1/ I
More informationChapter 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 informationPhysics 1A Lecture 10B
Physics 1A Lecture 10B "Sometimes the world puts a spin on life. When our equilibrium returns to us, we understand more because we've seen the whole picture. --Davis Barton Cross Products Another way to
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 informationLectures. Today: Rolling and Angular Momentum in ch 12. Complete angular momentum (chapter 12) and begin equilibrium (chapter 13)
Lectures Today: Rolling and Angular Momentum in ch 1 Homework 6 due Next time: Complete angular momentum (chapter 1) and begin equilibrium (chapter 13) By Monday, will post at website Sample midterm II
More informationYour Comments. That s the plan
Your Comments I love physics as much as the next gal, but I was wondering. Why don't we get class off the day after an evening exam? What if the ladder has friction with the wall? Things were complicated
More informationChapter 10. Rotation of a Rigid Object about a Fixed Axis
Chapter 10 Rotation of a Rigid Object about a Fixed Axis Angular Position Axis of rotation is the center of the disc Choose a fixed reference line. Point P is at a fixed distance r from the origin. A small
More informationForces of Rolling. 1) Ifobjectisrollingwith a com =0 (i.e.no netforces), then v com =ωr = constant (smooth roll)
Physics 2101 Section 3 March 12 rd : Ch. 10 Announcements: Mid-grades posted in PAW Quiz today I will be at the March APS meeting the week of 15-19 th. Prof. Rich Kurtz will help me. Class Website: http://www.phys.lsu.edu/classes/spring2010/phys2101-3/
More informationt = g = 10 m/s 2 = 2 s T = 2π g
Annotated Answers to the 1984 AP Physics C Mechanics Multiple Choice 1. D. Torque is the rotational analogue of force; F net = ma corresponds to τ net = Iα. 2. C. The horizontal speed does not affect the
More informationChapter 9- Static Equilibrium
Chapter 9- Static Equilibrium Changes in Office-hours The following changes will take place until the end of the semester Office-hours: - Monday, 12:00-13:00h - Wednesday, 14:00-15:00h - Friday, 13:00-14:00h
More informationPhysics 111. Lecture 22 (Walker: ) Torque Rotational Dynamics Static Equilibrium Oct. 28, 2009
Physics 111 Lecture 22 (Walker: 11.1-3) Torque Rotational Dynamics Static Equilibrium Oct. 28, 2009 Lecture 22 1/26 Torque (τ) We define a quantity called torque which is a measure of twisting effort.
More informationModels and Anthropometry
Learning Objectives Models and Anthropometry Readings: some of Chapter 8 [in text] some of Chapter 11 [in text] By the end of this lecture, you should be able to: Describe common anthropometric measurements
More informationCEE 271: Applied Mechanics II, Dynamics Lecture 25: Ch.17, Sec.4-5
1 / 36 CEE 271: Applied Mechanics II, Dynamics Lecture 25: Ch.17, Sec.4-5 Prof. Albert S. Kim Civil and Environmental Engineering, University of Hawaii at Manoa Date: 2 / 36 EQUATIONS OF MOTION: ROTATION
More informationPhysics 101: Lecture 15 Torque, F=ma for rotation, and Equilibrium
Physics 101: Lecture 15 Torque, F=ma for rotation, and Equilibrium Strike (Day 10) Prelectures, checkpoints, lectures continue with no change. Take-home quizzes this week. See Elaine Schulte s email. HW
More informationRotational Dynamics. Slide 2 / 34. Slide 1 / 34. Slide 4 / 34. Slide 3 / 34. Slide 6 / 34. Slide 5 / 34. Moment of Inertia. Parallel Axis Theorem
Slide 1 / 34 Rotational ynamics l Slide 2 / 34 Moment of Inertia To determine the moment of inertia we divide the object into tiny masses of m i a distance r i from the center. is the sum of all the tiny
More informationRotational Motion. Rotational Motion. Rotational Motion
I. Rotational Kinematics II. Rotational Dynamics (Netwton s Law for Rotation) III. Angular Momentum Conservation 1. Remember how Newton s Laws for translational motion were studied: 1. Kinematics (x =
More informationChapter 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 informationTranslational Motion Rotational Motion Equations Sheet
PHYSICS 01 Translational Motion Rotational Motion Equations Sheet LINEAR ANGULAR Time t t Displacement x; (x = rθ) θ Velocity v = Δx/Δt; (v = rω) ω = Δθ/Δt Acceleration a = Δv/Δt; (a = rα) α = Δω/Δt (
More informationPhysics 211 Week 10. Statics: Walking the Plank (Solution)
Statics: Walking the Plank (Solution) A uniform horizontal beam 8 m long is attached by a frictionless pivot to a wall. A cable making an angle of 37 o, attached to the beam 5 m from the pivot point, supports
More informationRotation Angular Momentum
Rotation Angular Momentum Lana Sheridan De Anza College Nov 28, 2017 Last time rolling motion Overview Definition of angular momentum relation to Newton s 2nd law angular impulse angular momentum of rigid
More informationTorque. Introduction. Torque. PHY torque - J. Hedberg
Torque PHY 207 - torque - J. Hedberg - 2017 1. Introduction 2. Torque 1. Lever arm changes 3. Net Torques 4. Moment of Rotational Inertia 1. Moment of Inertia for Arbitrary Shapes 2. Parallel Axis Theorem
More informationTorque and Static Equilibrium
Torque and Static Equilibrium Rigid Bodies Rigid body: An extended object in which the distance between any two points in the object is constant in time. Examples: sphere, disk Effect of external forces
More informationDefinition. is a measure of how much a force acting on an object causes that object to rotate, symbol is, (Greek letter tau)
Torque Definition is a measure of how much a force acting on an object causes that object to rotate, symbol is, (Greek letter tau) = r F = rfsin, r = distance from pivot to force, F is the applied force
More informationPhysics 2210 Homework 18 Spring 2015
Physics 2210 Homework 18 Spring 2015 Charles Jui April 12, 2015 IE Sphere Incline Wording A solid sphere of uniform density starts from rest and rolls without slipping down an inclined plane with angle
More informationTorque and Rotation Lecture 7
Torque and Rotation Lecture 7 ˆ In this lecture we finally move beyond a simple particle in our mechanical analysis of motion. ˆ Now we consider the so-called rigid body. Essentially, a particle with extension
More informationLecture 2 - Force Analysis
Lecture 2 - orce Analysis A Puzzle... Triangle or quadrilateral? 4 distinct points in a plane can either be arrange as a triangle with a point inside or as a quadrilateral. Extra Brownie Points: Use the
More informationChapter 10: Rotation
Chapter 10: Rotation Review of translational motion (motion along a straight line) Position x Displacement x Velocity v = dx/dt Acceleration a = dv/dt Mass m Newton s second law F = ma Work W = Fdcosφ
More informationUNIVERSITY OF TORONTO Faculty of Arts and Science
UNIVERSITY OF TORONTO Faculty of Arts and Science DECEMBER 2013 EXAMINATIONS PHY 151H1F Duration - 3 hours Attempt all questions. Each question is worth 10 points. Points for each part-question are shown
More information= o + t = ot + ½ t 2 = o + 2
Chapters 8-9 Rotational Kinematics and Dynamics Rotational motion Rotational motion refers to the motion of an object or system that spins about an axis. The axis of rotation is the line about which the
More 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 informationLecture 13 REVIEW. Physics 106 Spring What should we know? What should we know? Newton s Laws
Lecture 13 REVIEW Physics 106 Spring 2006 http://web.njit.edu/~sirenko/ What should we know? Vectors addition, subtraction, scalar and vector multiplication Trigonometric functions sinθ, cos θ, tan θ,
More informationFinal Exam Spring 2014 May 05, 2014
95.141 Final Exam Spring 2014 May 05, 2014 Section number Section instructor Last/First name Last 3 Digits of Student ID Number: Answer all questions, beginning each new question in the space provided.
More informationRutgers University Department of Physics & Astronomy. 01:750:271 Honors Physics I Fall Lecture 19. Home Page. Title Page. Page 1 of 36.
Rutgers University Department of Physics & Astronomy 01:750:271 Honors Physics I Fall 2015 Lecture 19 Page 1 of 36 12. Equilibrium and Elasticity How do objects behave under applied external forces? Under
More informationMoment of Inertia & Newton s Laws for Translation & Rotation
Moment of Inertia & Newton s Laws for Translation & Rotation In this training set, you will apply Newton s 2 nd Law for rotational motion: Στ = Σr i F i = Iα I is the moment of inertia of an object: I
More informationStatics. Phys101 Lectures 19,20. Key points: The Conditions for static equilibrium Solving statics problems Stress and strain. Ref: 9-1,2,3,4,5.
Phys101 Lectures 19,20 Statics Key points: The Conditions for static equilibrium Solving statics problems Stress and strain Ref: 9-1,2,3,4,5. Page 1 The Conditions for Static Equilibrium An object in static
More informationMomentum. The way to catch a knuckleball is to wait until it stops rolling and then pick it up. -Bob Uecker
Chapter 11 -, Chapter 11 -, Angular The way to catch a knuckleball is to wait until it stops rolling and then pick it up. -Bob Uecker David J. Starling Penn State Hazleton PHYS 211 Chapter 11 -, motion
More information= 2 5 MR2. I sphere = MR 2. I hoop = 1 2 MR2. I disk
A sphere (green), a disk (blue), and a hoop (red0, each with mass M and radius R, all start from rest at the top of an inclined plane and roll to the bottom. Which object reaches the bottom first? (Use
More informationHandout 7: Torque, angular momentum, rotational kinetic energy and rolling motion. Torque and angular momentum
Handout 7: Torque, angular momentum, rotational kinetic energy and rolling motion Torque and angular momentum In Figure, in order to turn a rod about a fixed hinge at one end, a force F is applied at a
More informationReview questions. Before the collision, 70 kg ball is stationary. Afterward, the 30 kg ball is stationary and 70 kg ball is moving to the right.
Review questions Before the collision, 70 kg ball is stationary. Afterward, the 30 kg ball is stationary and 70 kg ball is moving to the right. 30 kg 70 kg v (a) Is this collision elastic? (b) Find the
More informationChapter 10: Rotation. Chapter 10: Rotation
Chapter 10: Rotation Change in Syllabus: Only Chapter 10 problems (CH10: 04, 27, 67) are due on Thursday, Oct. 14. The Chapter 11 problems (Ch11: 06, 37, 50) will be due on Thursday, Oct. 21 in addition
More informationω = 0 a = 0 = α P = constant L = constant dt = 0 = d Equilibrium when: τ i = 0 τ net τ i Static Equilibrium when: F z = 0 F net = F i = ma = d P
Equilibrium when: F net = F i τ net = τ i a = 0 = α dp = 0 = d L = ma = d P = 0 = I α = d L = 0 P = constant L = constant F x = 0 τ i = 0 F y = 0 F z = 0 Static Equilibrium when: P = 0 L = 0 v com = 0
More informationStatic Equilibrium. Lecture 22. Chapter 12. Physics I Department of Physics and Applied Physics
Lecture 22 Chapter 12 Physics I 12.02.2013 Static Equilibrium Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsi Lecture Capture: http://echo360.uml.edu/danylov2013/physics1fall.html
More informationWelcome back to Physics 211
Welcome back to Physics 211 Today s agenda: Moment of Inertia Angular momentum 13-2 1 Current assignments Prelecture due Tuesday after Thanksgiving HW#13 due next Wednesday, 11/24 Turn in written assignment
More informationRecap I. Angular position: Angular displacement: s. Angular velocity: Angular Acceleration:
Recap I Angular position: Angular displacement: s Angular velocity: Angular Acceleration: Every point on a rotating rigid object has the same angular, but not the same linear motion! Recap II Circular
More informationChapters 10 & 11: Rotational Dynamics Thursday March 8 th
Chapters 10 & 11: Rotational Dynamics Thursday March 8 th Review of rotational kinematics equations Review and more on rotational inertia Rolling motion as rotation and translation Rotational kinetic energy
More informationCEE 271: Applied Mechanics II, Dynamics Lecture 28: Ch.17, Sec.2 3
1 / 20 CEE 271: Applied Mechanics II, Dynamics Lecture 28: Ch.17, Sec.2 3 Prof. Albert S. Kim Civil and Environmental Engineering, University of Hawaii at Manoa Monday, November 1, 2011 2 / 20 PLANAR KINETIC
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 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 informationStatic Equilibrium. Lana Sheridan. Dec 5, De Anza College
tatic Equilibrium Lana heridan De Anza College Dec 5, 2016 Last time simple harmonic motion Overview Introducing static equilibrium center of gravity tatic Equilibrium: ystem in Equilibrium Knowing that
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 informationRotational motion problems
Rotational motion problems. (Massive pulley) Masses m and m 2 are connected by a string that runs over a pulley of radius R and moment of inertia I. Find the acceleration of the two masses, as well as
More informationTranslational vs Rotational. m x. Connection Δ = = = = = = Δ = = = = = = Δ =Δ = = = = = 2 / 1/2. Work
Translational vs Rotational / / 1/ Δ m x v dx dt a dv dt F ma p mv KE mv Work Fd / / 1/ θ ω θ α ω τ α ω ω τθ Δ I d dt d dt I L I KE I Work / θ ω α τ Δ Δ c t s r v r a v r a r Fr L pr Connection Translational
More information. d. v A v B. e. none of these.
General Physics I Exam 3 - Chs. 7,8,9 - Momentum, Rotation, Equilibrium Oct. 28, 2009 Name Rec. Instr. Rec. Time For full credit, make your work clear to the grader. Show the formulas you use, the essential
More informationRolling without slipping Angular Momentum Conservation of Angular Momentum. Physics 201: Lecture 19, Pg 1
Physics 131: Lecture Today s Agenda Rolling without slipping Angular Momentum Conservation o Angular Momentum Physics 01: Lecture 19, Pg 1 Rolling Without Slipping Rolling is a combination o rotation and
More informationPhysics 2210 Fall smartphysics Conservation of Angular Momentum 11/20/2015
Physics 2210 Fall 2015 smartphysics 19-20 Conservation of Angular Momentum 11/20/2015 Poll 11-18-03 In the two cases shown above identical ladders are leaning against frictionless walls and are not sliding.
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, 8-9 pm in NSC 118/119 Sunday, 6:30-8 pm in CCLIR 468 Announcements This
More informationAnnouncements Oct 17, 2013
Announcements Oct 17, 2013 1. No announcements! Colton - Lecture 14 - pg 1 Real satellites: http://science.nasa.gov/realtime/jtrack/3d/jtrack3d.html International space station, 340.5 km above surface
More informationPhysics 141. Lecture 18. Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester, Lecture 18, Page 1
Physics 141. Lecture 18. Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester, Lecture 18, Page 1 Physics 141. Lecture 18. Course Information. Topics to be discussed today: A
More informationPhysics A - PHY 2048C
Physics A - PHY 2048C and 11/15/2017 My Office Hours: Thursday 2:00-3:00 PM 212 Keen Building Warm-up Questions 1 Did you read Chapter 12 in the textbook on? 2 Must an object be rotating to have a moment
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 informationLECTURE 22 EQUILIBRIUM. Instructor: Kazumi Tolich
LECTURE 22 EQUILIBRIUM Instructor: Kazumi Tolich Lecture 22 2 Reading chapter 11-3 to 11-4 Static equilibrium Center of mass and balance Static equilibrium 3 If a rigid object is in equilibrium (constant
More informationPhysics 141 Rotational Motion 2 Page 1. Rotational Motion 2
Physics 141 Rotational Motion 2 Page 1 Rotational Motion 2 Right handers, go over there, left handers over here. The rest of you, come with me.! Yogi Berra Torque Motion of a rigid body, like motion of
More informationCenter of Gravity. The location of the center of gravity is defined by: n mgx. APSC 111 Review Page 7
Center of Gravity We have said that for rigid bodies, all of the forces act at the centre of mass. This is a normally a very good approximation, but strictly speaking, the forces act at the centre of gravity,
More informationPhysics 8 Wednesday, October 30, 2013
Physics 8 Wednesday, October 30, 2013 HW9 (due Friday) is 7 conceptual + 8 calculation problems. Of the 8 calculation problems, 4 or 5 are from Chapter 11, and 3 or 4 are from Chapter 12. 7pm HW sessions:
More informationω avg [between t 1 and t 2 ] = ω(t 1) + ω(t 2 ) 2
PHY 302 K. Solutions for problem set #9. Textbook problem 7.10: For linear motion at constant acceleration a, average velocity during some time interval from t 1 to t 2 is the average of the velocities
More information