The University of Melbourne Engineering Mechanics
|
|
- Shanon Ross
- 5 years ago
- Views:
Transcription
1 The University of Melbourne Engineering Mechanics Tutorial Eleven Instantaneous Centre and General Motion Part A (Introductory) 1. (Problem 5/93 from Meriam and Kraige - Dynamics) For the instant represented in Figure 1, corner A of the rectangular plate has a velocity v A = 2.8 m/s and the plate has a clockwise angular velocity ω = 12 rad/s. Determine: (a) the distance between A and the instantaneous centre C (of zero velocity); (b) the distance between B and the instantaneous centre C; and (c) the magnitude of the corresponding velocity of point B. 2. (Problem 5/127 from Meriam and Kraige - Dynamics) The 9 m steel beam is being hoisted from its horizontal position by the two cables attached at A and B. If the initial angular accelerations of the hoisting drums are α 1 = 0.5 rad/s 2 and α 2 = 0.2 rad/s 2 in the directions shown in Figure 2, determine: (a) the corresponding angular acceleration α of the beam,; (b) the acceleration of C; and (c) and the distance b from B to a point P on the beam centerline which has no acceleration. 3. (Problem 5/128 from Meriam and Kraige - Dynamics) A car has a forward acceleration a = 4 m/s 2 without slipping its 600 mm diameter tyres. When a point P on the tire in the position shown in Figure 3 have zero horizontal component of acceleration, determine: Figure 1: Rectangle plate 1
2 Figure 2: Hoisted beam Figure 3: Tyre (a) the tangential component of relative acceleration (a P/O ) t ; (b) the normal component of relative acceleration (a P/O ) n ; and (c) the velocity v of the car. 4. (Problem 6/1, 6/2 from Meriam and Kraige - Dynamics) (a) Accelerating frame (b) Overhead monorail system Figure 4: Accelerating objects (a) The uniform 30 kg bar OB shown in Figure 4(a) is secured in the vertical position to the accelerating frame by the hinge at O and the roller at A. If the horizontal acceleration of the frame is a = 20 m/s 2, compute the force F A on the roller; (b) and the horizontal component of the force supported by the pin at O. Page 2 of 8
3 (c) A passenger car of an overhead monorail system is driven by one of its two small wheels A or B (see Figure 4(b)). Select the one for which the car can be given the greater acceleration without slipping the driving wheel and compute the maximum acceleration if the effective coefficient of friction is limited to 0.25 between the wheels and the rail. Neglect the small mass of the wheels. 5. (Problem 6/35, 6/36 from Meriam and Kraige - Dynamics) (a) Hinged plate (b) Automotive dynamometer Figure 5: Hinged plate and automotive dynamometer (a) The 20 kg uniform steel plate is freely hinged about the z-axis as shown in Figure 5(a). Calculate the tangential acceleration of the mass centre of the plate when it is released from rest in the horizontal y-z plane; and (b) calculate the force supported by each of the bearings at A and B at this instant. (c) The automotive dynamometer is able to simulate road conditions for an acceleration of 0.6g for the loaded pickup truck with a total mass of 2.8 Mg (see Figure 5(b)). Calculate the required moment of inertia of the dynamometer drum about its centre O assuming that the drum turns freely during the acceleration phase of the test. 6. (Problem 6/76, 6/86 from Meriam and Kraige - Dynamics) (a) The 30 kg solid circular disk is initially at rest on the horizontal surface when a 12 N force P, constant in magnitude and direction, is applied to the cord wrapped securely around its periphery (see Figure 6(a)). Friction between the disc and the surface is negligible. Calculate the linear velocity v of the centre of the disk after it has moved 1.2 metres from rest; and (b) find the angular velocity ω of the disk after the 12 N force has been applied for 2 seconds. Page 3 of 8
4 (a) Circular disc (b) Hoisted beam Figure 6: Circular disc and hoisted beam (c) The 3.6 m steel beam shown in Figure 6(b) has a mass of 125 kg and is hoisted from rest where the tension in each of the cables is 613 N. If the hoisting drums are given initial angular accelerations α 1 = 4 rad/s 2 and α 2 = 6 rad/s 2, calculate the corresponding tensions T A and T B in the cables. The beam may be treated as a slender bar. Part B 7. (Problem 5/95, 5/97, 5/98 from Meriam and Kraige - Dynamics) (a) The bar AB shown in Figure 7(a) has a counterclockwise angular velocity of 6 rad/s. Construct the velocity vectors for points A and G of the bar and specify their magnitudes if the instantaneous centre of zero velocity for the bar is (a) at C 1, (b) at C 2, and (c) at C 3. (b) At a certain instant vertex B of the right-triangular plate has a velocity of 200 mm/s in the direction shown in Figure 7(b). If the instantaneous centre of zero velocity for the plate is 40 mm from point B and if the angular velocity of the plate is clockwise, determine the velocity of point D. (c) A car mechanic walks two wheel/tyre units across a horizontal floor as shown in Figure 7(c). He walks with constant speed v and keeps the tires in the configuration shown with the same position relative to his body. If there is no slipping at any interface, determine (a) the angular velocity of the lower tyre, (b) the angular velocity of the upper tyre, and (c) the velocities of points A, B, C, and D. The radius of both tires is r. Page 4 of 8
5 (a) Bar (b) Right-triangular plate (c) Rolling wheels Figure 7: Instantaneous centre problems 8. (Problem 5/129, 5/135 from Meriam and Kraige - Dynamics) (a) The centre O of the disk has the velocity and acceleration shown in Figure 8(a). If the disc rolls without slipping on the horizontal surface, determine the velocity of A and the acceleration of B for the instant represented. (b) If the velocity of point A is 3 m/s to the right and is constant for an interval including the position shown in Figure 8(b), determine the tangential acceleration of point B along its path and the angular acceleration of the bar. 9. (Problem 5/145 from Meriam and Kraige - Dynamics) If OA in the linkage shown in Figure 9 has a constant counterclockwise angular velocity ω 0 = 10 rad/s, calculate the angular acceleration of link AB for the position where the coordinates of A are x = 60 mm and y = 80 mm. Link BC is vertical for this position. Solve by vector algebra. Given that v BC = 5.83k rad/s and v AB = 2.5k rad/s.) 10. (Problem 5/146 from Meriam and Kraige - Dynamics) The revolving crank ED and connecting link CD cause the rigid frame ABO to oscillate about O (see Figure 10). For the instant represented ED and CD are both perpendicular to F O, and the crank ED has an angular velocity of 0.4 rad/s and an angular acceleration of 0.06 rad/s 2, both counterclockwise. For this instant determine the acceleration of point A with respect to point B. Page 5 of 8
6 (a) Disc (b) Bar Figure 8: Disc and bar Figure 9: Linkage 11. (Problem 6/18 from Meriam and Kraige - Dynamics) The device shown in Figure 11 oscillates horizontally according to x = b sin ωt, where b and ω are constants. Determine and plot the force T in the light link at A as a function of the time t. The mass of the uniform slender rod AP is m. 12. (Problem 6/29 from Meriam and Kraige - Dynamics) Determine the maximum mass m of the cylinder for which the loaded 2000 kg coal car will not overturn about the rear wheels B (see Figure 12). Neglect the mass of all pulleys and wheels. (Note that the tension in the cable at C is not 2mg.) 13. (Problem 6/54 from Meriam and Kraige - Dynamics) A device for impact testing consists of a 34 kg pendulum with mass centre at G and with radius of gyration about O of 620 mm (see Figure 13). The distance b for the pendulum is selected so that the force on the bearing at O has the least possible value during impact with the specimen at the Page 6 of 8
7 Figure 10: Crank Figure 11: Oscillating device Figure 12: Coal car Figure 13: Impact testing machine Page 7 of 8
8 Figure 14: Coal car Figure 15: Dump truck bottom of the swing. Determine b and calculate the magnitude of the total force R on the bearing O an instant after release from rest at θ = (Problem 6/55 from Meriam and Kraige - Dynamics) The 12 kg cylinder supported by the bearing brackets at A and B has a moment of inertia about the vertical z 0 -axis through its mass centre G equal to kgm 2 (see Figure 14). The disk and brackets have a moment of inertia about the vertical z-axis of rotation equal to 0.60 kgm 2. If a torque M = 16 Nm is applied to the disk through its shaft with the disc initially at rest, calculate the horizontal x-components of force supported by the bearings at A and B. 15. (Problem 6/105 from Meriam and Kraige - Dynamics) The hydraulic cylinder BC of the dump truck is broken and is disconnected (see Figure 15). The driver (who has passed a course in dynamics) decides to calculate the minimum acceleration a of the truck required to tilt the dump about its pivot at A. He then proceeds to calculate the initial angular acceleration α of the dump if the truck is given an acceleration of 1.2a. What are his correct answers for a and α, and would he be able to carry out the experiment? The dump container may be modelled as a homogeneous and solid rectangular block with mass centre at G. Page 8 of 8
5. Plane Kinetics of Rigid Bodies
5. Plane Kinetics of Rigid Bodies 5.1 Mass moments of inertia 5.2 General equations of motion 5.3 Translation 5.4 Fixed axis rotation 5.5 General plane motion 5.6 Work and energy relations 5.7 Impulse
More information16.07 Dynamics Final Exam
Name:... Massachusetts Institute of Technology 16.07 Dynamics Final Exam Tuesday, December 20, 2005 Problem 1 (8) Problem 2 (8) Problem 3 (10) Problem 4 (10) Problem 5 (10) Problem 6 (10) Problem 7 (10)
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 informationDynamics Plane kinematics of rigid bodies Section 4: TJW Rotation: Example 1
Section 4: TJW Rotation: Example 1 The pinion A of the hoist motor drives gear B, which is attached to the hoisting drum. The load L is lifted from its rest position and acquires an upward velocity of
More informationPlane Motion of Rigid Bodies: Forces and Accelerations
Plane Motion of Rigid Bodies: Forces and Accelerations Reference: Beer, Ferdinand P. et al, Vector Mechanics for Engineers : Dynamics, 8 th Edition, Mc GrawHill Hibbeler R.C., Engineering Mechanics: Dynamics,
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 informationRotation. PHYS 101 Previous Exam Problems CHAPTER
PHYS 101 Previous Exam Problems CHAPTER 10 Rotation Rotational kinematics Rotational inertia (moment of inertia) Kinetic energy Torque Newton s 2 nd law Work, power & energy conservation 1. Assume that
More informationSOLUTION di x = y2 dm. rdv. m = a 2 bdx. = 2 3 rpab2. I x = 1 2 rp L0. b 4 a1 - x2 a 2 b. = 4 15 rpab4. Thus, I x = 2 5 mb2. Ans.
17 4. Determine the moment of inertia of the semiellipsoid with respect to the x axis and express the result in terms of the mass m of the semiellipsoid. The material has a constant density r. y x y a
More informationFinal Exam April 30, 2013
Final Exam Instructions: You have 120 minutes to complete this exam. This is a closed-book, closed-notes exam. You are allowed to use a calculator during the exam. Usage of mobile phones and other electronic
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 informationCHAPTER 8: ROTATIONAL OF RIGID BODY PHYSICS. 1. Define Torque
7 1. Define Torque 2. State the conditions for equilibrium of rigid body (Hint: 2 conditions) 3. Define angular displacement 4. Define average angular velocity 5. Define instantaneous angular velocity
More information1 MR SAMPLE EXAM 3 FALL 2013
SAMPLE EXAM 3 FALL 013 1. A merry-go-round 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 informationDYNAMICS ME HOMEWORK PROBLEM SETS
DYNAMICS ME 34010 HOMEWORK PROBLEM SETS Mahmoud M. Safadi 1, M.B. Rubin 2 1 safadi@technion.ac.il, 2 mbrubin@technion.ac.il Faculty of Mechanical Engineering Technion Israel Institute of Technology Spring
More informationProblems. B 60 mm. 80 mm. 80 mm. 120 mm
roblems roblem 4.1 When the power to an electric motor is turned on, the motor reaches its rated speed of 3300 rpm in 6 s, and when the power is turned off, the motor coasts to rest in 80 s. ssume uniformly
More informationTOPIC E: OSCILLATIONS EXAMPLES SPRING Q1. Find general solutions for the following differential equations:
TOPIC E: OSCILLATIONS EXAMPLES SPRING 2019 Mathematics of Oscillating Systems Q1. Find general solutions for the following differential equations: Undamped Free Vibration Q2. A 4 g mass is suspended by
More informationName: Date: Period: AP Physics C Rotational Motion HO19
1.) A wheel turns with constant acceleration 0.450 rad/s 2. (9-9) 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 informationDynamics of Rotation
Dynamics of Rotation 1 Dynamic of Rotation Angular velocity and acceleration are denoted ω and α respectively and have units of rad/s and rad/s. Relationship between Linear and Angular Motions We can show
More informationUNIVERSITY OF SASKATCHEWAN GE MECHANICS III FINAL EXAM APRIL 18, 2011 Professor A. Dolovich A CLOSED BOOK EXAMINATION TIME: 3 HOURS
UNIVERSITY OF SASKATCHEWAN GE 226.3 MECHANICS III FINAL EXAM APRIL 18, 2011 Professor A. Dolovich A CLOSED BOOK EXAMINATION TIME: 3 HOURS LAST NAME (printed): FIRST NAME (printed): STUDENT NUMBER: EXAMINATION
More informationPROBLEM 16.4 SOLUTION
PROBLEM 16.4 The motion of the.5-kg rod AB is guided b two small wheels which roll freel in horizontal slots. If a force P of magnitude 8 N is applied at B, determine (a) the acceleration of the rod, (b)
More informationTOPIC D: ROTATION EXAMPLES SPRING 2018
TOPIC D: ROTATION EXAMPLES SPRING 018 Q1. A car accelerates uniformly from rest to 80 km hr 1 in 6 s. The wheels have a radius of 30 cm. What is the angular acceleration of the wheels? Q. The University
More informationExam 3 April 16, 2014
Exam 3 Instructions: You have 60 minutes to complete this exam. This is a closed-book, closed-notes exam. You are allowed to use a calculator during the exam. Usage of mobile phones and other electronic
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 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 0.30-m-radius automobile
More informationDynamics Kinetics of a particle Section 4: TJW Force-mass-acceleration: Example 1
Section 4: TJW Force-mass-acceleration: Example 1 The beam and attached hoisting mechanism have a combined mass of 1200 kg with center of mass at G. If the inertial acceleration a of a point P on the hoisting
More informationMechanics Topic D (Rotation) - 1 David Apsley
TOPIC D: ROTATION SPRING 2019 1. Angular kinematics 1.1 Angular velocity and angular acceleration 1.2 Constant-angular-acceleration formulae 1.3 Displacement, velocity and acceleration in circular motion
More informationForce and Moment. Figure 1 Figure 2
Force and Moment 1 Determine the magnitude and direction of the resultant of the two forces shown, using (a) the parallelogram law (b) the sine law. [1391 N, 47.8 ] Figure 1 Figure 2 2 The force F of magnitude
More informationPLANAR RIGID BODY MOTION: TRANSLATION &
PLANAR RIGID BODY MOTION: TRANSLATION & Today s Objectives : ROTATION Students will be able to: 1. Analyze the kinematics of a rigid body undergoing planar translation or rotation about a fixed axis. In-Class
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 informationUNIVERSITI TUN HUSSEIN ONN MALAYSIA FINAL EXAMINATION SEMESTER I SESSION 2009/2010
Aftisse^ UNIVERSITI TUN HUSSEIN ONN MALAYSIA SEMESTER I SESSION 2009/2010 SUBJECT : DYNAMICS SUBJECT CODE : BDA2013 COURSE : 2 BDD DATE : NOVEMBER 2009 DURATION : 2 */ 2 HOURS INSTRUCTION : ANSWER FOUR
More informationEQUATIONS OF MOTION: GENERAL PLANE MOTION (Section 17.5) Today s Objectives: Students will be able to analyze the planar kinetics of a rigid body
EQUATIONS OF MOTION: GENERAL PLANE MOTION (Section 17.5) Today s Objectives: Students will be able to analyze the planar kinetics of a rigid body undergoing general plane motion. APPLICATIONS As the soil
More informationTUTORIAL SHEET 1. magnitude of P and the values of ø and θ. Ans: ø =74 0 and θ= 53 0
TUTORIAL SHEET 1 1. The rectangular platform is hinged at A and B and supported by a cable which passes over a frictionless hook at E. Knowing that the tension in the cable is 1349N, determine the moment
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 informationSTATICS. Friction VECTOR MECHANICS FOR ENGINEERS: Eighth Edition CHAPTER. Ferdinand P. Beer E. Russell Johnston, Jr.
Eighth E 8 Friction CHAPTER VECTOR MECHANICS FOR ENGINEERS: STATICS Ferdinand P. Beer E. Russell Johnston, Jr. Lecture Notes: J. Walt Oler Texas Tech University Contents Introduction Laws of Dry Friction.
More informationSECTION A. 8 kn/m. C 3 m 3m
SECTION Question 1 150 m 40 kn 5 kn 8 kn/m C 3 m 3m D 50 ll dimensions in mm 15 15 Figure Q1(a) Figure Q1(b) The horizontal beam CD shown in Figure Q1(a) has a uniform cross-section as shown in Figure
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 informationb) Fluid friction: occurs when adjacent layers in a fluid are moving at different velocities.
Ch.6 Friction Types of friction a) Dry friction: occurs when non smooth (non ideal) surfaces of two solids are in contact under a condition of sliding or a tendency to slide. (also called Coulomb friction)
More informationPhys101 Third Major-161 Zero Version Coordinator: Dr. Ayman S. El-Said Monday, December 19, 2016 Page: 1
Coordinator: Dr. Ayman S. El-Said Monday, December 19, 2016 Page: 1 Q1. A water molecule (H 2 O) consists of an oxygen (O) atom of mass 16m and two hydrogen (H) atoms, each of mass m, bound to it (see
More information7.6 Journal Bearings
7.6 Journal Bearings 7.6 Journal Bearings Procedures and Strategies, page 1 of 2 Procedures and Strategies for Solving Problems Involving Frictional Forces on Journal Bearings For problems involving a
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 informationWhen a rigid body is in equilibrium, both the resultant force and the resultant couple must be zero.
When a rigid body is in equilibrium, both the resultant force and the resultant couple must be zero. 0 0 0 0 k M j M i M M k R j R i R F R z y x z y x Forces and moments acting on a rigid body could be
More informationSample 5. Determine the tension in the cable and the horizontal and vertical components of reaction at the pin A. Neglect the size of the pulley.
Sample 1 The tongs are designed to handle hot steel tubes which are being heat-treated in an oil bath. For a 20 jaw opening, what is the minimum coefficient of static friction between the jaws and the
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 information5.2 Rigid Bodies and Two-Dimensional Force Systems
5.2 Rigid odies and Two-Dimensional Force Systems 5.2 Rigid odies and Two-Dimensional Force Systems Procedures and Strategies, page 1 of 1 Procedures and Strategies for Solving Problems Involving Equilibrium
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 informationRotation. Rotational Variables
Rotation Rigid Bodies Rotation variables Constant angular acceleration Rotational KE Rotational Inertia Rotational Variables Rotation of a rigid body About a fixed rotation axis. Rigid Body an object that
More informationChapter Rotational Motion
26 Chapter Rotational Motion 1. Initial angular velocity of a circular disc of mass M is ω 1. Then two small spheres of mass m are attached gently to diametrically opposite points on the edge of the disc.
More informationME 274: Basic Mechanics II Spring April 18, Problem 1 (24 points):
Problem 1 (24 points): Given: The block shown in the figure slides on a smooth surface. A thin homogenous bar is attached to the block and is free to rotate about a pin joint at A. At the instant shown
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 informationCHAPTER 10 ROTATION OF A RIGID OBJECT ABOUT A FIXED AXIS WEN-BIN JIAN ( 簡紋濱 ) DEPARTMENT OF ELECTROPHYSICS NATIONAL CHIAO TUNG UNIVERSITY
CHAPTER 10 ROTATION OF A RIGID OBJECT ABOUT A FIXED AXIS WEN-BIN JIAN ( 簡紋濱 ) DEPARTMENT OF ELECTROPHYSICS NATIONAL CHIAO TUNG UNIVERSITY OUTLINE 1. Angular Position, Velocity, and Acceleration 2. Rotational
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 5-kilogram sphere is connected to a 10-kilogram sphere by a rigid rod of negligible
More informationDYNAMICS MOMENT OF INERTIA
DYNAMICS MOMENT OF INERTIA S TO SELF ASSESSMENT EXERCISE No.1 1. A cylinder has a mass of 1 kg, outer radius of 0.05 m and radius of gyration 0.03 m. It is allowed to roll down an inclined plane until
More informationif the initial displacement and velocities are zero each. [ ] PART-B
Set No - 1 I. Tech II Semester Regular Examinations ugust - 2014 ENGINEERING MECHNICS (Common to ECE, EEE, EIE, io-tech, E Com.E, gri. E) Time: 3 hours Max. Marks: 70 Question Paper Consists of Part- and
More informationMechatronics. MANE 4490 Fall 2002 Assignment # 1
Mechatronics MANE 4490 Fall 2002 Assignment # 1 1. For each of the physical models shown in Figure 1, derive the mathematical model (equation of motion). All displacements are measured from the static
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 informationSOLUTION 8 1. a+ M B = 0; N A = 0. N A = kn = 16.5 kn. Ans. + c F y = 0; N B = 0
8 1. The mine car and its contents have a total mass of 6 Mg and a center of gravity at G. If the coefficient of static friction between the wheels and the tracks is m s = 0.4 when the wheels are locked,
More informationRotation review packet. Name:
Rotation review packet. Name:. A pulley of mass m 1 =M and radius R is mounted on frictionless bearings about a fixed axis through O. A block of equal mass m =M, suspended by a cord wrapped around the
More informationProblem Set x Classical Mechanics, Fall 2016 Massachusetts Institute of Technology. 1. Moment of Inertia: Disc and Washer
8.01x Classical Mechanics, Fall 2016 Massachusetts Institute of Technology Problem Set 10 1. Moment of Inertia: Disc and Washer (a) A thin uniform disc of mass M and radius R is mounted on an axis passing
More informationMoment of Inertia Race
Review Two points, A and B, are on a disk that rotates with a uniform speed about an axis. Point A is closer to the axis than point B. Which of the following is NOT true? 1. Point B has the greater tangential
More information1. Replace the given system of forces acting on a body as shown in figure 1 by a single force and couple acting at the point A.
Code No: Z0321 / R07 Set No. 1 I B.Tech - Regular Examinations, June 2009 CLASSICAL MECHANICS ( Common to Mechanical Engineering, Chemical Engineering, Mechatronics, Production Engineering and Automobile
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 information1 Problems 1-3 A disc rotates about an axis through its center according to the relation θ (t) = t 4 /4 2t
Slide 1 / 30 1 Problems 1-3 disc rotates about an axis through its center according to the relation θ (t) = t 4 /4 2t etermine the angular velocity of the disc at t= 2 s 2 rad/s 4 rad/s 6 rad/s 8 rad/s
More informationSlide 1 / 30. Slide 2 / 30. Slide 3 / m/s -1 m/s
1 Problems 1-3 disc rotates about an axis through its center according to the relation θ (t) = t 4 /4 2t Slide 1 / 30 etermine the angular velocity of the disc at t= 2 s 2 rad/s 4 rad/s 6 rad/s 8 rad/s
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 informationPHY 001 (Physics I) Lecture 7
PHY 001 (Physics I) Instructor: Dr. Mohamed Fouad Salem mohamed.salem@gmail.com Textbook University Physics, 12 th edition, Young and Freedman Course Material Website http://meryesk.wordpress.com/phy001/
More informationSuggested Problems. Chapter 1
Suggested Problems Ch1: 49, 51, 86, 89, 93, 95, 96, 102. Ch2: 9, 18, 20, 44, 51, 74, 75, 93. Ch3: 4, 14, 46, 54, 56, 75, 91, 80, 82, 83. Ch4: 15, 59, 60, 62. Ch5: 14, 52, 54, 65, 67, 83, 87, 88, 91, 93,
More informationPhysics 12. Unit 5 Circular Motion and Gravitation Part 1
Physics 12 Unit 5 Circular Motion and Gravitation Part 1 1. Nonlinear motions According to the Newton s first law, an object remains its tendency of motion as long as there is no external force acting
More 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 informationPhys101 Lectures 19, 20 Rotational Motion
Phys101 Lectures 19, 20 Rotational Motion Key points: Angular and Linear Quantities Rotational Dynamics; Torque and Moment of Inertia Rotational Kinetic Energy Ref: 10-1,2,3,4,5,6,8,9. Page 1 Angular Quantities
More informationSlide 1 / 133. Slide 2 / 133. Slide 3 / How many radians are subtended by a 0.10 m arc of a circle of radius 0.40 m?
1 How many radians are subtended by a 0.10 m arc of a circle of radius 0.40 m? Slide 1 / 133 2 How many degrees are subtended by a 0.10 m arc of a circle of radius of 0.40 m? Slide 2 / 133 3 A ball rotates
More informationSlide 2 / 133. Slide 1 / 133. Slide 3 / 133. Slide 4 / 133. Slide 5 / 133. Slide 6 / 133
Slide 1 / 133 1 How many radians are subtended by a 0.10 m arc of a circle of radius 0.40 m? Slide 2 / 133 2 How many degrees are subtended by a 0.10 m arc of a circle of radius of 0.40 m? Slide 3 / 133
More informationStatics Chapter II Fall 2018 Exercises Corresponding to Sections 2.1, 2.2, and 2.3
Statics Chapter II Fall 2018 Exercises Corresponding to Sections 2.1, 2.2, and 2.3 2 3 Determine the magnitude of the resultant force FR = F1 + F2 and its direction, measured counterclockwise from the
More informationKinematics, Dynamics, and Vibrations FE Review Session. Dr. David Herrin March 27, 2012
Kinematics, Dynamics, and Vibrations FE Review Session Dr. David Herrin March 7, 0 Example A 0 g ball is released vertically from a height of 0 m. The ball strikes a horizontal surface and bounces back.
More informationSOLUTION 8 7. To hold lever: a+ M O = 0; F B (0.15) - 5 = 0; F B = N. Require = N N B = N 0.3. Lever,
8 3. If the coefficient of static friction at is m s = 0.4 and the collar at is smooth so it only exerts a horizontal force on the pipe, determine the minimum distance x so that the bracket can support
More informationTable of Contents. Pg. # Momentum & Impulse (Bozemanscience Videos) Lab 2 Determination of Rotational Inertia 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 tatics
More informationEngineering Mechanics. Friction in Action
Engineering Mechanics Friction in Action What is friction? Friction is a retarding force that opposes motion. Friction types: Static friction Kinetic friction Fluid friction Sources of dry friction Dry
More information4.0 m s 2. 2 A submarine descends vertically at constant velocity. The three forces acting on the submarine are viscous drag, upthrust and weight.
1 1 wooden block of mass 0.60 kg is on a rough horizontal surface. force of 12 N is applied to the block and it accelerates at 4.0 m s 2. wooden block 4.0 m s 2 12 N hat is the magnitude of the frictional
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 informationWhen a rigid body is in equilibrium, both the resultant force and the resultant couple must be zero.
When a rigid body is in equilibrium, both the resultant force and the resultant couple must be zero. 0 0 0 0 k M j M i M M k R j R i R F R z y x z y x Forces and moments acting on a rigid body could be
More informationAt the highest point on its trajectory the radius of curvature of the path of the projectile in problem 1 (above) would be:
A projectile fired at 30 from the horizontal v 40 m / s with an initial velocity of 40 meters per second will reach a maximum height H above the horizontal of: 30 " 1 -,H a. 81.5 m d. _ 24.8 m b. _ 20.4
More informationMOI (SEM. II) EXAMINATION.
Problems Based On Centroid And MOI (SEM. II) EXAMINATION. 2006-07 1- Find the centroid of a uniform wire bent in form of a quadrant of the arc of a circle of radius R. 2- State the parallel axis theorem.
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 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 informationCutnell/Johnson Physics
Cutnell/Johnson Physics Classroom Response System Questions Chapter 9 Rotational Dynamics Interactive Lecture Questions 9.1.1. You are using a wrench in an attempt to loosen a nut by applying a force as
More informationEQUATIONS OF MOTION: ROTATION ABOUT A FIXED AXIS (Section 17.4) Today s Objectives: Students will be able to analyze the planar kinetics of a rigid
EQUATIONS OF MOTION: ROTATION ABOUT A FIXED AXIS (Section 17.4) Today s Objectives: Students will be able to analyze the planar kinetics of a rigid body undergoing rotational motion. APPLICATIONS The crank
More informationVALLIAMMAI ENGINEERING COLLEGE SRM NAGAR, KATTANKULATHUR DEPARTMENT OF MECHANICAL ENGINEERING
VALLIAMMAI ENGINEERING COLLEGE SRM NAGAR, KATTANKULATHUR 603203 DEPARTMENT OF MECHANICAL ENGINEERING BRANCH: MECHANICAL YEAR / SEMESTER: I / II UNIT 1 PART- A 1. State Newton's three laws of motion? 2.
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 informationEquilibrium of a Rigid Body. Engineering Mechanics: Statics
Equilibrium of a Rigid Body Engineering Mechanics: Statics Chapter Objectives Revising equations of equilibrium of a rigid body in 2D and 3D for the general case. To introduce the concept of the free-body
More informationFigure 1 Answer: = m
Q1. Figure 1 shows a solid cylindrical steel rod of length =.0 m and diameter D =.0 cm. What will be increase in its length when m = 80 kg block is attached to its bottom end? (Young's modulus of steel
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 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 informationLecture D20-2D Rigid Body Dynamics: Impulse and Momentum
J Peraire 1607 Dynamics Fall 004 Version 11 Lecture D0 - D Rigid Body Dynamics: Impulse and Momentum In lecture D9, we saw the principle of impulse and momentum applied to particle motion This principle
More informationSample Final Exam 02 Physics 106 (Answers on last page)
Sample Final Exam 02 Physics 106 (Answers on last page) Name (Print): 4 Digit ID: Section: Instructions: 1. There are 30 multiple choice questions on the test. There is no penalty for guessing, so you
More informationB) v `2. C) `2v. D) 2v. E) 4v. A) 2p 25. B) p C) 2p. D) 4p. E) 4p 2 25
1. 3. A ball attached to a string is whirled around a horizontal circle of radius r with a tangential velocity v. If the radius is changed to 2r and the magnitude of the centripetal force is doubled the
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 informationAssignment 9. to roll without slipping, how large must F be? Ans: F = R d mgsinθ.
Assignment 9 1. A heavy cylindrical container is being rolled up an incline as shown, by applying a force parallel to the incline. The static friction coefficient is µ s. The cylinder has radius R, mass
More informationAP practice ch 7-8 Multiple Choice
AP practice ch 7-8 Multiple Choice 1. A spool of thread has an average radius of 1.00 cm. If the spool contains 62.8 m of thread, how many turns of thread are on the spool? "Average radius" allows us to
More informationBalancing of Masses. 1. Balancing of a Single Rotating Mass By a Single Mass Rotating in the Same Plane
lecture - 1 Balancing of Masses Theory of Machine Balancing of Masses A car assembly line. In this chapter we shall discuss the balancing of unbalanced forces caused by rotating masses, in order to minimize
More informationENGINEERING COUNCIL CERTIFICATE LEVEL MECHANICAL AND STRUCTURAL ENGINEERING C105 TUTORIAL 13 - MOMENT OF INERTIA
ENGINEERING COUNCIL CERTIFICATE LEVEL MECHANICAL AND STRUCTURAL ENGINEERING C15 TUTORIAL 1 - MOMENT OF INERTIA This tutorial covers essential material for this exam. On completion of this tutorial you
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 informationPlanar Rigid Body Kinematics Homework
Chapter 2: Planar Rigid ody Kinematics Homework Chapter 2 Planar Rigid ody Kinematics Homework Freeform c 2018 2-1 Chapter 2: Planar Rigid ody Kinematics Homework 2-2 Freeform c 2018 Chapter 2: Planar
More information