We define angular displacement, θ, and angular velocity, ω. What's a radian?


 Samuel Dawson
 11 months ago
 Views:
Transcription
1 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 is  1
2 Consider purely angular measures for 1 revolution ω = Δ θ Δt recall 2
3 "Suggested " problems for Thursday.... page 101: 34, 37 page 202: 1, 8, 11, 13, 14, 18 Problems if you want extra practice.... page 202: 3, 10, 15, 16, 19, 21 3
4 Rotation of a Rigid Body Translation  the object as a whole moves along a trajectory, but does not rotate. Rotation  the object rotates about a fixed point. Every point on the object moves in a circle. During uniform rotation of a rigid body  every point on the body has the same angular velocity, ω, and the same angular displacement, θ θ= ω t true for both the red and green points v = ωr & v = ωr but v v linear velocities are not the same 4
5 Angular Acceleration  if you push on the edge of a bicycle wheel it begins to rotate, if you continue to push is rotates faster. recall linear acceleration was defined By analogy we define angular acceleration, α, as Linear and Circular Motion Variables standard units: m, m/s, m/s 2 standard units: rad, rad/s, rad/s 2 5
6 Linear and Circular Motion Equations v 2  v o 2 = 2a(xx o ) ω 2 ω ο 2 = 2α(θ θ ο ) 1 The disk in a computer disk drive spins up to 5400 rpm in 2.00 seconds. What is the angular acceleration, α, of the disk? (give answer to 3 sig figs and in standard units) 6
7 2 For the same computer disk, at the end of 2 seconds what angle, θ, has the disk turned through? (The disk in a computer disk drive spins up to 5400 rpm in 2.00 seconds.) (standard units and 3 sig figs) a c = v 2 /r  the acceleration an object in uniform circular motion undergoes  and a c is always directed toward the center of the circle. Uniform Circular Motion implies ω = 0, so α = 0. But we have just discussed a case where α what does this mean for a c? 7
8 the acceleration has 2 components: the a c from before and a t, tangential acceleration a t is in the same direction as the velocity and is what caused v to increase. a t = v/ t = ( ω/ t)r a t = αr 8
9 x = rθ v = rω a t = rα a c = 0α = 0 3 A ball on the end of string swings in a horizontal circle once every second. The magnitude of which of the following is zero. Choose all the correct quantities. A B Velocity Angular Velocity C Centripetal Acceleration D E Angular Acceleration Tangential Acceleration 9
10 4 A ball on the end of string swings in a horizontal circle once every second. The magnitude of which of the following is constant, but not zero. Choose all the correct quantities. A B C D E Velocity Angular Velocity Centripetal Acceleration Angular Acceleration Tangential Acceleration Torque  the rotational analog of force 1. the magnitude of the force the ability of a force to cause rotation depends on 3 factors: 2. the distance, r, from the pivot point that the force is applied 3. the angle, φ, at which the force is applied 10
11 τ = r x F τ = rfsinθ, with the direction given by the RHR i x i = j x j = k x k = 0 i x j = k j x k = i k x i = j j x i = k k x j = i i x k = j 11
12 5 In trying to open a door, Ryan pushes perpendicular to the door's surface with a force of 240N at a distance of 75 cm from the hinges. What torque does Ryan exert on the door? (standard units and 2 sig figs) 6 Lulu uses a 20 cm long wrench to turn a nut. The wrench handle is tilted 30 o above the horizontal and Lulu pulls straight down on the end with a force of 100N. How much torque does Lulu exert on the nut? (standard units, 2 sig figs) 12
13 7 Which has the largest torque? The rods all have the same length and are pivoted at the dot. A B 2 N 2 N C 2 N D 4 N E 45 o 4 N 8 Which has the smallest torque? The rods all have the same length and are pivoted at the dot. A B 2 N 2 N C 2 N D 4 N E 45 o 4 N 13
14 Net Torque r = 10 cm 9 Two forces act on the wheel shown. What third force, acting at point P, will make the net torque on the wheel zero? P Pivot A B C D E 14
15 Page 232: 3, 5, 6, 7, 8, 10, 13, 14 F T m A tangential force, F, exerts a torque on the particle of mass, m, and causes a tangential acceleration, a t the torque is given by: how is this related to a t? 15
16 What if there is more than on particle in motion? 16
17 We define the moment of inertia, I, as I = Σm i r i 2 so that Στ = Iα Στ = Iα I = Σm i r i 2 Recall: ΣF = ma What is the significance of the moment of inertia? 17
18 An object with a large moment of inertia is hard to start rotating (and to stop) and vice versa. Depends not only on how much mass, but how the mass is distributed. The further the mass is from the axis of rotation the larger I is and the more torque is needed to make the object rotate. 18
19 Moments for common shapes (calculated from r 2 dm) 1 Which will roll faster down a hill? A B cylindrical hoop cylindrical disk 19
20 An engine on a small airplane is specified to have a torque of 500N. m. This engine drives a 2.0 m, 40 kg single blade propeller. On start up, how long does it take the propeller to reach 2000 rpm? Conditions of Equilibrium 20
21 Consider a 100 N, 3.0 m long ladder supported by two sawhorse, placed at one end and 1 meter from the other end. What forces do the sawhorses exert on the ladder? What is the minimum value of the coefficient of friction so that a 3.0 m long ladder, inclined at an angle of 60 o will not slip? 21
22 Try this with a soda can. Center of Gravity  the point where the force of gravity exerts no torque 22
23 A 10 kg mass hangs from a pulley on a rope. The pulley is 2.00kg and has a radius of 10.0 cm. Find the tension in the rope and the acceleration of the mass. Angular Momentum for a single mass recall p = mv l = r x p = m r x v for a rigid body L = Iω 23
24 An ice skater spins around on the tips of her blades while holding a 5.0 kg mass in each hand. She begins with her hand outstretched and her hands 140 cm apart. While spinning at 2.0 rev/s she pulls the masses in a holds them 50 cm apart against his shoulders. If we neglect the mass of the skater how fast is she spinning after pulling the masses in? Angular Momentum recall: p = mv by direct analogy L = Iω Conservation of Angular Momentum L is conserved if τ net = 0 24
25 Page 234: 26, 30, 32, 34 Page 291: 30, 32 25
Chapter 10. Rotation
Chapter 10 Rotation Rotation Rotational Kinematics: Angular velocity and Angular Acceleration Rotational Kinetic Energy Moment of Inertia Newton s nd Law for Rotation Applications MFMcGrawPHY 45 Chap_10HaRotationRevised
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 informationChapter 6, Problem 18. Agenda. Rotational Inertia. Rotational Inertia. Calculating Moment of Inertia. Example: Hoop vs.
Agenda Today: Homework quiz, moment of inertia and torque Thursday: Statics problems revisited, rolling motion Reading: Start Chapter 8 in the reading Have to cancel office hours today: will have extra
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 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 informationExercise Torque Magnitude Ranking Task. Part A
Exercise 10.2 Calculate the net torque about point O for the two forces applied as in the figure. The rod and both forces are in the plane of the page. Take positive torques to be counterclockwise. τ 28.0
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 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 informationPhysics 23 Exam 3 April 2, 2009
1. A string is tied to a doorknob 0.79 m from the hinge as shown in the figure. At the instant shown, the force applied to the string is 5.0 N. What is the torque on the door? A) 3.3 N m B) 2.2 N m C)
More informationChapter 12. Rotation of a Rigid Body
Chapter 12. Rotation of a Rigid Body Not all motion can be described as that of a particle. Rotation requires the idea of an extended object. This diver is moving toward the water along a parabolic trajectory,
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 informationPhys 106 Practice Problems Common Quiz 1 Spring 2003
Phys 106 Practice Problems Common Quiz 1 Spring 2003 1. For a wheel spinning with constant angular acceleration on an axis through its center, the ratio of the speed of a point on the rim to the speed
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 informationPhysics for Scientist and Engineers third edition Rotational Motion About a Fixed Axis Problems
A particular bird s eye can just distinguish objects that subtend an angle no smaller than about 3 E 4 rad, A) How many degrees is this B) How small an object can the bird just distinguish when flying
More informationPS 11 GeneralPhysics I for the Life Sciences
PS 11 GeneralPhysics I for the Life Sciences ROTATIONAL MOTION D R. B E N J A M I N C H A N A S S O C I A T E P R O F E S S O R P H Y S I C S D E P A R T M E N T F E B R U A R Y 0 1 4 Questions and Problems
More informationAngular velocity and angular acceleration CHAPTER 9 ROTATION. Angular velocity and angular acceleration. ! equations of rotational motion
Angular velocity and angular acceleration CHAPTER 9 ROTATION! r i ds i dθ θ i Angular velocity and angular acceleration! equations of rotational motion Torque and Moment of Inertia! Newton s nd Law for
More informationAP Physics. Harmonic Motion. Multiple Choice. Test E
AP Physics Harmonic Motion Multiple Choice Test E A 0.10Kg block is attached to a spring, initially unstretched, of force constant k = 40 N m as shown below. The block is released from rest at t = 0 sec.
More informationBasics of rotational motion
Basics of rotational motion Motion of bodies rotating about a given axis, like wheels, blades of a fan and a chair cannot be analyzed by treating them as a point mass or particle. At a given instant of
More information1301W.600 Lecture 16. November 6, 2017
1301W.600 Lecture 16 November 6, 2017 You are Cordially Invited to the Physics Open House Friday, November 17 th, 2017 4:308:00 PM Tate Hall, Room B20 Time to apply for a major? Consider Physics!! Program
More information3. A bicycle tire of radius 0.33 m and a mass 1.5 kg is rotating at 98.7 rad/s. What torque is necessary to stop the tire in 2.0 s?
Practice 8A Torque 1. Find the torque produced by a 3.0 N force applied at an angle of 60.0 to a door 0.25 m from the hinge. What is the maximum torque this force could exert? 2. If the torque required
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 informationPhysics A  PHY 2048C
Physics A  PHY 2048C and 11/15/2017 My Office Hours: Thursday 2:003:00 PM 212 Keen Building Warmup Questions 1 Did you read Chapter 12 in the textbook on? 2 Must an object be rotating to have a moment
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 informationAdvanced Higher Physics. Rotational motion
Wallace Hall Academy Physics Department Advanced Higher Physics Rotational motion Problems AH Physics: Rotational Motion 1 2013 Data Common Physical Quantities QUANTITY SYMBOL VALUE Gravitational acceleration
More informationPhysics 53 Exam 3 November 3, 2010 Dr. Alward
1. When the speed of a reardrive car (a car that's driven forward by the rear wheels alone) is increasing on a horizontal road the direction of the frictional force on the tires is: A) forward for all
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 information1.1. Rotational Kinematics Description Of Motion Of A Rotating Body
PHY 19 PHYSICS III 1. Moment Of Inertia 1.1. Rotational Kinematics Description Of Motion Of A Rotating Body 1.1.1. Linear Kinematics Consider the case of linear kinematics; it concerns the description
More informationPhysics 131: Lecture 21. Today s Agenda
Physics 131: Lecture 21 Today s Agenda Rotational dynamics Torque = I Angular Momentum Physics 201: Lecture 10, Pg 1 Newton s second law in rotation land Sum of the torques will equal the moment of inertia
More informationFIGURE 2. Total Acceleration The direction of the total acceleration of a rotating object can be found using the inverse tangent function.
Take it Further Demonstration Versus Angular Speed Purpose Show that tangential speed depends on radius. Materials two tennis balls attached to different lengths of string (approx. 1.0 m and 1.5 m) Procedure
More informationPhysics 131: Lecture 21. Today s Agenda
Physics 131: Lecture 1 Today s Agenda Rotational dynamics Torque = I Angular Momentum Physics 01: Lecture 10, Pg 1 Newton s second law in rotation land Sum of the torques will equal the moment of inertia
More informationFALL TERM EXAM, PHYS 1211, INTRODUCTORY PHYSICS I Saturday, 14 December 2013, 1PM to 4 PM, AT 1003
FALL TERM EXAM, PHYS 1211, INTRODUCTORY PHYSICS I Saturday, 14 December 2013, 1PM to 4 PM, AT 1003 NAME: STUDENT ID: INSTRUCTION 1. This exam booklet has 14 pages. Make sure none are missing 2. There is
More information= y(x, t) =A cos (!t + kx)
A harmonic wave propagates horizontally along a taut string of length L = 8.0 m and mass M = 0.23 kg. The vertical displacement of the string along its length is given by y(x, t) = 0. m cos(.5 t + 0.8
More informationConcept Question: Normal Force
Concept Question: Normal Force Consider a person standing in an elevator that is accelerating upward. The upward normal force N exerted by the elevator floor on the person is 1. larger than 2. identical
More information112 A General Method, and Rolling without Slipping
112 A General Method, and Rolling without Slipping Let s begin by summarizing a general method for analyzing situations involving Newton s Second Law for Rotation, such as the situation in Exploration
More information(a) On the dots below that represent the students, draw and label freebody diagrams showing the forces on Student A and on Student B.
2003 B1. (15 points) A rope of negligible mass passes over a pulley of negligible mass attached to the ceiling, as shown above. One end of the rope is held by Student A of mass 70 kg, who is at rest on
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 10 ROTATION OF A RIGID OBJECT ABOUT A FIXED AXIS WENBIN JIAN ( 簡紋濱 ) DEPARTMENT OF ELECTROPHYSICS NATIONAL CHIAO TUNG UNIVERSITY
CHAPTER 10 ROTATION OF A RIGID OBJECT ABOUT A FIXED AXIS WENBIN JIAN ( 簡紋濱 ) DEPARTMENT OF ELECTROPHYSICS NATIONAL CHIAO TUNG UNIVERSITY OUTLINE 1. Angular Position, Velocity, and Acceleration 2. Rotational
More informationSummer Physics 41 Pretest. Shorty Shorts (2 pts ea): Circle the best answer. Show work if a calculation is required.
Summer Physics 41 Pretest Name: Shorty Shorts (2 pts ea): Circle the best answer. Show work if a calculation is required. 1. An object hangs in equilibrium suspended by two identical ropes. Which rope
More informationConcepTest PowerPoints
ConcepTest PowerPoints Chapter 8 Physics: Principles with Applications, 6 th edition Giancoli 2005 Pearson Prentice Hall This work is protected by United States copyright laws and is provided solely for
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 informationDescription: Using conservation of energy, find the final velocity of a "yo yo" as it unwinds under the influence of gravity.
Chapter 10 [ Edit ] Overview Summary View Diagnostics View Print View with Answers Chapter 10 Due: 11:59pm on Sunday, November 6, 2016 To understand how points are awarded, read the Grading Policy for
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 informationChapter 10 Rotational Kinematics and Energy. Copyright 2010 Pearson Education, Inc.
Chapter 10 Rotational Kinematics and Energy Copyright 010 Pearson Education, Inc. 101 Angular Position, Velocity, and Acceleration Copyright 010 Pearson Education, Inc. 101 Angular Position, Velocity,
More informationLecture 11  Advanced Rotational Dynamics
Lecture 11  Advanced Rotational Dynamics A Puzzle... A moldable blob of matter of mass M and uniform density is to be situated between the planes z = 0 and z = 1 so that the moment of inertia around the
More information4) Vector = and vector = What is vector = +? A) B) C) D) E)
1) Suppose that an object is moving with constant nonzero acceleration. Which of the following is an accurate statement concerning its motion? A) In equal times its speed changes by equal amounts. B) In
More informationExam 3 Practice Solutions
Exam 3 Practice Solutions Multiple Choice 1. A thin hoop, a solid disk, and a solid sphere, each with the same mass and radius, are at rest at the top of an inclined plane. If all three are released at
More informationA uniform rod of length L and Mass M is attached at one end to a frictionless pivot. If the rod is released from rest from the horizontal position,
A dentist s drill starts from rest. After 3.20 s of constant angular acceleration, it turns at a rate of 2.51 10 4 rev/min. (a) Find the drill s angular acceleration. (b) Determine the angle (in radians)
More informationName Student ID Score Last First. I = 2mR 2 /5 around the sphere s center of mass?
NOTE: ignore air resistance in all Questions. In all Questions choose the answer that is the closest!! Question I. (15 pts) Rotation 1. (5 pts) A bowling ball that has an 11 cm radius and a 7.2 kg mass
More informationChapter 12 Torque Pearson Education, Inc.
Chapter 12 Torque Schedule 3Nov torque 12.15 5Nov torque 12.68 10Nov fluids 18.18 12Nov periodic motion 15.17 17Nov waves in 1D 16.16 19Nov waves in 2D, 3D 16.79, 17.13 24Nov gravity 13.18
More informationCentripetal force keeps an object in circular motion Rotation and Revolution
Centripetal force keeps an object in circular motion. 10.1 Rotation and Revolution Two types of circular motion are and. An is the straight line around which rotation takes place. When an object turns
More informationInClass Problems 3032: Moment of Inertia, Torque, and Pendulum: Solutions
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.01 TEAL Fall Term 004 InClass Problems 303: Moment of Inertia, Torque, and Pendulum: Solutions Problem 30 Moment of Inertia of a
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 information第 1 頁, 共 7 頁 Chap10 1. Test Bank, Question 3 One revolution per minute is about: 0.0524 rad/s 0.105 rad/s 0.95 rad/s 1.57 rad/s 6.28 rad/s 2. *Chapter 10, Problem 8 The angular acceleration of a wheel
More informationLecture 14 Feb
Lecture 14 Feb.12. 2016. Moving in circles Angular momentum Spinning at the Olympics Torques Why is a wrench useful? Center of Gravity Useful info for crossing Niagara falls on a wire The New Hubble Telescope
More informationThe Arctic is Melting
The Arctic is Melting 1 Arctic sea has shown a large drop in area over the last thirty years. Japanese and US satellite data Jerry Gilfoyle The Arctic and the Length of Day 1 / 42 The Arctic is Melting
More informationPhysics 106 Common Exam 2: March 5, 2004
Physics 106 Common Exam 2: March 5, 2004 Signature Name (Print): 4 Digit ID: Section: Instructions: nswer all questions. Questions 1 through 10 are multiple choice questions worth 5 points each. You may
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 information10 ROTATIONAL MOTION AND ANGULAR MOMENTUM
Chapter 10 Rotational Motion and Angular Momentum 395 10 ROTATIONAL MOTION AND ANGULAR MOMENTUM Figure 10.1 The mention of a tornado conjures up images of raw destructive power. Tornadoes blow houses away
More informationPhysics 221. Exam III Spring f S While the cylinder is rolling up, the frictional force is and the cylinder is rotating
Physics 1. Exam III Spring 003 The situation below refers to the next three questions: A solid cylinder of radius R and mass M with initial velocity v 0 rolls without slipping up the inclined plane. N
More informationLecture PowerPoints. Chapter 10 Physics for Scientists and Engineers, with Modern Physics, 4 th edition Giancoli
Lecture PowerPoints Chapter 10 Physics for Scientists and Engineers, with Modern Physics, 4 th edition Giancoli 2009 Pearson Education, Inc. This work is protected by United States copyright laws and is
More informationSolution Only gravity is doing work. Since gravity is a conservative force mechanical energy is conserved:
8) roller coaster starts with a speed of 8.0 m/s at a point 45 m above the bottom of a dip (see figure). Neglecting friction, what will be the speed of the roller coaster at the top of the next slope,
More informationPHYS 1303 Final Exam Example Questions
PHYS 1303 Final Exam Example Questions (In summer 2014 we have not covered questions 3035,40,41) 1.Which quantity can be converted from the English system to the metric system by the conversion factor
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 informationAP Physics C: Rotation II. (Torque and Rotational Dynamics, Rolling Motion) Problems
AP Physics C: Rotation II (Torque and Rotational Dynamics, Rolling Motion) Problems 1980M3. A billiard ball has mass M, radius R, and moment of inertia about the center of mass I c = 2 MR²/5 The ball is
More informationChapter 12. Recall that when a spring is stretched a distance x, it will pull back with a force given by: F = kx
Chapter 1 Lecture Notes Chapter 1 Oscillatory Motion Recall that when a spring is stretched a distance x, it will pull back with a force given by: F = kx When the mass is released, the spring will pull
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 informationTHE TWENTYSECOND ANNUAL SLAPT PHYSICS CONTEST SOUTHERN ILLINOIS UNIVERSITY EDWARDSVILLE APRIL 21, 2007 MECHANICS TEST. g = 9.
THE TWENTYSECOND ANNUAL SLAPT PHYSICS CONTEST SOUTHERN ILLINOIS UNIVERSITY EDWARDSVILLE APRIL 21, 27 MECHANICS TEST g = 9.8 m/s/s Please answer the following questions on the supplied answer sheet. You
More informationSimple and Physical Pendulums Challenge Problem Solutions
Simple and Physical Pendulums Challenge Problem Solutions Problem 1 Solutions: For this problem, the answers to parts a) through d) will rely on an analysis of the pendulum motion. There are two conventional
More information10 ROTATIONAL MOTION AND ANGULAR MOMENTUM
CHAPTER 10 ROTATIONAL MOTION AND ANGULAR MOMENTUM 317 10 ROTATIONAL MOTION AND ANGULAR MOMENTUM Figure 10.1 The mention of a tornado conjures up images of raw destructive power. Tornadoes blow houses away
More informationChapter 9 [ Edit ] Ladybugs on a Rotating Disk. v = ωr, where r is the distance between the object and the axis of rotation. Chapter 9. Part A.
Chapter 9 [ Edit ] Chapter 9 Overview Summary View Diagnostics View Print View with Answers Due: 11:59pm on Sunday, October 30, 2016 To understand how points are awarded, read the Grading Policy for this
More informationPhysics 130: Questions to study for midterm #1 from Chapter 8
Physics 130: Questions to study for midterm #1 from Chapter 8 1. If the beaters on a mixer make 800 revolutions in 5 minutes, what is the average rotational speed of the beaters? a. 2.67 rev/min b. 16.8
More informationRevolve, Rotate & Roll:
I. WarmUP. Revolve, Rotate & Roll: Physics 203, Yaverbaum John Jay College of Criminal Justice, the CUNY Given g, the rate of freefall acceleration near Earth s surface, and r, the radius of a VERTICAL
More information9. h = R. 10. h = 3 R
Version PREVIEW Torque Chap. 8 sizeore (13756) 1 This printout should have 3 questions. ultiplechoice questions ay continue on the next colun or page find all choices before answering. Note in the dropped
More informationr r Sample Final questions for PS 150
Sample Final questions for PS 150 1) Which of the following is an accurate statement? A) Rotating a vector about an axis passing through the tip of the vector does not change the vector. B) The magnitude
More informationPh1a: Solution to the Final Exam Alejandro Jenkins, Fall 2004
Ph1a: Solution to the Final Exam Alejandro Jenkins, Fall 2004 Problem 1 (10 points)  The Delivery A crate of mass M, which contains an expensive piece of scientific equipment, is being delivered to Caltech.
More informationUniform Circular Motion:Circular motion is said to the uniform if the speed of the particle (along the circular path) remains constant.
Circular Motion: Uniform Circular Motion:Circular motion is said to the uniform if the speed of the particle (along the circular path) remains constant. Angular Displacement: Scalar form:?s = r?θ Vector
More information= F 4. O Which force produces the greatest torque about the point O (marked by the blue dot)? E. not enough information given to decide
Q10.1 The four forces shown all have the same magnitude: F 1 = F 2 = F 3 = F 4. F 1 F 3 O Which force produces the greatest torque about the point O (marked by the blue dot)? F 2 F 4 A. F 1 B. F 2 C. F
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 122 1 Midterm 3 Thursday April 13th Material covered: Ch 9 Ch 12 Lectures
More informationWritten Homework problems. Spring (taken from Giancoli, 4 th edition)
Written Homework problems. Spring 014. (taken from Giancoli, 4 th edition) HW1. Ch1. 19, 47 19. Determine the conversion factor between (a) km / h and mi / h, (b) m / s and ft / s, and (c) km / h and m
More informationPHY218 SPRING 2016 Review for Final Exam: Week 14 Final Review: Chapters 111, 1314
Final Review: Chapters 111, 1314 These are selected problems that you are to solve independently or in a team of 23 in order to better prepare for your Final Exam 1 Problem 1: Chasing a motorist This
More informationEnergy problems look like this: Momentum conservation problems. Example 81. Momentum is a VECTOR Example 82
Review Chp 7: Accounting with Mechanical Energy: the overall Bank Balance When we judge how much energy a system has, we must have two categories: Kinetic energy (K sys ), and potential energy (U sys ).
More information1 of 16 3/23/2016 3:09 PM Practice Exam Chapters 69 (Ungraded) (3103258) Due: Wed Apr 6 2016 06:00 PM EDT Question 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Description This will
More informationWork and kinetic Energy
Work and kinetic Energy Problem 66. M=4.5kg r = 0.05m I = 0.003kgm 2 Q: What is the velocity of mass m after it dropped a distance h? (No friction) h m=0.6kg mg Work and kinetic Energy Problem 66. M=4.5kg
More informationChap. 10: Rotational Motion
Chap. 10: Rotational Motion I. Rotational Kinematics II. Rotational Dynamics  Newton s Law for Rotation III. Angular Momentum Conservation (Chap. 10) 1 Newton s Laws for Rotation n e t I 3 rd part [N
More informationRadians & Radius. Circumference = 2πr Part s = θ r r. θ=s/r. θ in radians! 360 o =2π rad = 6.28 rad θ (rad) = π/180 o θ (deg)
Radians & Radius Circumference = 2πr Part s = θ r r s θ θ in radians! 360 o =2π rad = 6.28 rad θ (rad) = π/180 o θ (deg) θ=s/r 1 Angular speed and acceleration θ f ϖ = t ω = f lim Δt 0 θ t i i Δθ Δt =
More informationCircular Motion and Universal Law of Gravitation. 8.01t Oct 4, 2004
Circular Motion and Universal Law of Gravitation 8.01t Oct 4, 2004 Summary: Circular Motion arc length s= Rθ tangential velocity ds v = = dt dθ R = Rω dt 2 d θ 2 dt tangential acceleration a θ = dv θ =
More informationRotational Motion. 1 Purpose. 2 Theory 2.1 Equation of Motion for a Rotating Rigid Body
Rotational Motion Equipment: Capstone, 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 cm bead
More information= constant of gravitation is G = N m 2 kg 2. Your goal is to find the radius of the orbit of a geostationary satellite.
Problem 1 Earth and a Geostationary Satellite (10 points) The earth is spinning about its axis with a period of 3 hours 56 minutes and 4 seconds. The equatorial radius of the earth is 6.38 10 6 m. The
More informationVersion A (01) Question. Points
Question Version A (01) Version B (02) 1 a a 3 2 a a 3 3 b a 3 4 a a 3 5 b b 3 6 b b 3 7 b b 3 8 a b 3 9 a a 3 10 b b 3 11 b b 8 12 e e 8 13 a a 4 14 c c 8 15 c c 8 16 a a 4 17 d d 8 18 d d 8 19 a a 4
More informationRotational & RigidBody Mechanics. Lectures 3+4
Rotational & RigidBody Mechanics Lectures 3+4 Rotational Motion So far: point objects moving through a trajectory. Next: moving actual dimensional objects and rotating them. 2 Circular Motion  Definitions
More informationPLANAR KINETICS OF A RIGID BODY: WORK AND ENERGY Today s Objectives: Students will be able to: 1. Define the various ways a force and couple do work.
PLANAR KINETICS OF A RIGID BODY: WORK AND ENERGY Today s Objectives: Students will be able to: 1. Define the various ways a force and couple do work. InClass Activities: 2. Apply the principle of work
More informationPhys 270 Final Exam. Figure 1: Question 1
Phys 270 Final Exam Time limit: 120 minutes Each question worths 10 points. Constants: g = 9.8m/s 2, G = 6.67 10 11 Nm 2 kg 2. 1. (a) Figure 1 shows an object with moment of inertia I and mass m oscillating
More informationEquilibrium. For an object to remain in equilibrium, two conditions must be met. The object must have no net force: and no net torque:
Equilibrium For an object to remain in equilibrium, two conditions must be met. The object must have no net force: F v = 0 and no net torque: v τ = 0 Worksheet A uniform rod with a length L and a mass
More informationChapter 7 Rotational Motion 7.1 Angular Quantities Homework # 51
7.1 Angular Quantities Homework # 51 01. Convert the following angle measurements to radians. a.) 30.0 b.) 45.0 c.) 90.0 02. The Empire State Building has a total height of 443.2 m (including the lightning
More informationAP Physics 1 Chapter 7 Circular Motion and Gravitation
AP Physics 1 Chapter 7 Circular Motion and Gravitation Chapter 7: Circular Motion and Angular Measure Gravitation Angular Speed and Velocity Uniform Circular Motion and Centripetal Acceleration Angular
More informationChapter 11. Today. Last Wednesday. Precession from Pre lecture. Solving problems with torque
Chapter 11 Last Wednesday Solving problems with torque Work and power with torque Angular momentum Conserva5on of angular momentum Today Precession from Pre lecture Study the condi5ons for equilibrium
More informationSCHOOL OF COMPUTING, ENGINEERING AND MATHEMATICS SEMESTER 1 EXAMINATIONS 2012/2013 XE121. ENGINEERING CONCEPTS (Test)
s SCHOOL OF COMPUTING, ENGINEERING AND MATHEMATICS SEMESTER EXAMINATIONS 202/203 XE2 ENGINEERING CONCEPTS (Test) Time allowed: TWO hours Answer: Attempt FOUR questions only, a maximum of TWO questions
More informationPhysics A  PHY 2048C
Physics A  PHY 2048C Newton s Laws & Equations of 09/27/2017 My Office Hours: Thursday 2:003:00 PM 212 Keen Building Warmup Questions 1 In uniform circular motion (constant speed), what is the direction
More informationω = ω 0 θ = θ + ω 0 t αt ( ) Rota%onal Kinema%cs: ( ONLY IF α = constant) v = ω r ω ω r s = θ r v = d θ dt r = ω r + a r = a a tot + a t = a r
θ (t) ( θ 1 ) Δ θ = θ 2 s = θ r ω (t) = d θ (t) dt v = d θ dt r = ω r v = ω r α (t) = d ω (t) dt = d 2 θ (t) dt 2 a tot 2 = a r 2 + a t 2 = ω 2 r 2 + αr 2 a tot = a t + a r = a r ω ω r a t = α r ( ) Rota%onal
More informationCircular motion, Center of Gravity, and Rotational Mechanics
Circular motion, Center of Gravity, and Rotational Mechanics Rotation and Revolution Every object moving in a circle turns around an axis. If the axis is internal to the object (inside) then it is called
More information