PROBLEM 16.4 SOLUTION

Size: px
Start display at page:

Download "PROBLEM 16.4 SOLUTION"

Transcription

1 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) the reactions at A and B. (a) Σ F =Σ ( F ) : P = ma P 8N a = = = 3.0 m/s m.5 kg a = 3.0 m/s (b) r r Σ MB =Σ( MB) : Wr Ar = ma π π Σ F = 0: A+ B W = 0 A = W 1 ma mg 1 P π π = π π = (.5 kg)(9.81 m/s ) 1 (8 N) π π = 8.91 N N = N A = 3.8 N B= W A= (.5)(9.81) 3.819, B = 0.71 N PROPRIETARY MATERIAL. 013 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual ma be displaed, 1407

2 PROBLEM The triangular weldment ABC is guided b two pins that slide freel in parallel curved slots of radius 6 in. cut in a vertical plate. The weldment weighs 16 lb and its mass center is located at Point G. Knowing that at the instant shown the velocit of each pin is 30 in./s downward along the slots, determine (a) the acceleration of the weldment, (b) the reactions at A and B. Slot: v = 30 in./s a n n v (30 in./s) = = = 150 in./s r 6in. a =1.5 ft/s 30 a t = at 60 Weldment is in translation a n =1.5 ft/s 60 Σ F =Σ F : mg cos30 = mat a t = ft/s 60 (a) Acceleration 1 an β = tan = tan = 4.14 a = t + n a a a t = (7.886) + (1.5) a = ft/s 84.1 a = 30.6 ft/s 84.1 PROPRIETARY MATERIAL. 013 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual ma be displaed, 148

3 PROBLEM (Continued) (b) Reactions 16 lb ma = (30.56 ft/s ) = lb 3. ft/s Σ M =Σ ( M ) : A A B cos30 (9 in.) (16 lb)(6 in.) = ( lb)(cos84.14 )(3 in.) ( lb)(sin84.14 )(6 in.) 7.794B 96 = B = lb B = 1.85 lb 30 Σ F =Σ ( F ) : Acos30 + Bcos30 = macos84.14 Acos30 + (1.85 lb)cos30 = ( lb)cos84.14 Acos lb = lb A = lb A = lb 30 PROPRIETARY MATERIAL. 013 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual ma be displaed, 149

4 PROBLEM 16.5 The rotor of an electric motor has an angular velocit of 3600 rpm when the load and power are cut off. The 50-kg rotor, which has a centroidal radius of gration of 180 mm, then coasts to rest. Knowing that kinetic friction results in a couple of magnitude 3.5 N m eerted on the rotor, determine the number of revolutions that the rotor eecutes before coming to rest. I = mk = (50)(0.180) = 1.6 kg m M = Iα: 3.5 N m = (1.6 kg m ) α 0 3 α =.1605 rad/s (deceleration) π ω0 = 3600 rpm 60 = 10 π rad/s ω = ω + αθ 0 = (10π rad/s) + (.1605 rad/s ) θ θ = rad = rev or θ = 530 rev PROPRIETARY MATERIAL. 013 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual ma be displaed, 1439

5 PROBLEM A uniform slender rod AB rests on a frictionless horizontal surface, and a force P of magnitude 0.5 lb is applied at A in a direction perpendicular to the rod. Knowing that the rod weighs 1.75 lb, determine (a) the acceleration of Point A, (b) the acceleration of Point B, (c) the location of the point on the bar that has zero acceleration. W m = g 1 W I = 1 g L W Σ F =Σ ( F) : P = ma = a g P 0.5 lb 1 a = g = g = g W 1.75 lb 7 a = 1 7 g L 1 W Σ MG =Σ ( MG) : P = Iα = Lα 1 g P 5 0.5lb g 6 g α = 6 = 6 = WL 1.75 lb L 7 L 6 g α = 7 L We calculate the accelerations immediatel after the force is applied. After the rod acquires angular velocit, there will be additional normal accelerations. (a) Acceleration of Point A. L aa = a + α = + = = (b) Acceleration of Point B. 1 L (3. ft/s g g g ) L ab = a α = = = L 6 (3. ft/s g g g ) a = ft/s A a = 9.0 ft/s B PROPRIETARY MATERIAL. 013 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual ma be displaed, 1478

6 PROBLEM (Continued) (c) Point of zero acceleration. Since zg = 1 L ap = 0 a ( z z ) α = 0 P G 1 a g 7 P G 6 g α 7 L 1 z z = = = L zp = L+ L= L 6 3 zp = (36 in.) 3 z P = 4.0 in. PROPRIETARY MATERIAL. 013 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual ma be displaed, 1479

7 PROBLEM The 80-g o-o shown has a centroidal radius of gration of 30 mm. The radius of the inner drum on which a string is wound is 6 mm. Knowing that at the instant shown the acceleration of the center of the o-o is 1 m/s upward, determine (a) the required tension T in the string, (b) the corresponding angular acceleration of the o-o. W = mg W = kg (9.81 m/s ) = N W Σ F =Σ( F) : T W = a g T (0.08 kg)(9.81 m/s ) = (0.08 kg)(1 m/s ) T = N (a) Tension in the string. T = N Σ M =Σ ( M ) : Tr = Iα G G (b) Angular acceleration. ( N)(0.006 m) = mk α N m = (0.08 kg)(0.03 m) α α = rad/s α = 7.1 rad/s PROPRIETARY MATERIAL. 013 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual ma be displaed, 1488

8 PROBLEM A beam AB of mass m and of uniform cross section is suspended from two springs as shown. If spring breaks, determine at that instant (a) the angular acceleration of the beam, (b) the acceleration of Point A, (c) the acceleration of Point B. (a) mg Σ F = = ma 3 mg L 1 Σ MG = mlα 3 = 1 G g a G =, 3 g α = L (b) a A = g g L + 3 L g = 3, (c) a B = g g L + 3 L = 5g 3 g a A = 3 5g a B = 3 PROPRIETARY MATERIAL. 013 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual ma be displaed, 1499

9 PROBLEM A uniform slender rod of length L = 900 mm and mass m = 4 kg is suspended from a hinge at C. A horizontal force P of magnitude 75 N is applied at end B. Knowing that r = 5 mm, determine (a) the angular acceleration of the rod, (b) the components of the reaction at C. (a) Angular acceleration. 1 a = rα I = ml 1 L Σ MC =Σ ( MC) : Pr + = ( ma) r + Iα 1 = ( mrα) r + ml α 1 L 1 Pr + = m r + L α m 1 Substitute data: (75 N) 0.5 m + = (4 kg) (0.5 m) + (0.9 m) α = 0.475α (b) Components of reaction at C. Σ F =Σ( F ) : C W = 0 α = rad/s α = rad/s C = W = mg = (4 kg)(9.81 m/s ) C = 39. N Σ F =Σ( F ) : C P = ma C = P ma = P m( rα) = 75 N (4 kg)(0.5 m)( rad/s ) C = 75 N 96.4 N = 1.4 N C 1.4 N = PROPRIETARY MATERIAL. 013 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual ma be displaed, 157

10 PROBLEM A 1-lb uniform plate rotates about A in a vertical plane under the combined ect of gravit and of the vertical force P. Knowing that at the instant shown the plate has an angular velocit of 0 rad/s and an angular acceleration of 30 rad/s both counterclockwise, determine (a) the force P, (b) the components of the reaction at A. Kinematics. Mass and moment of inertia. 6 ft (30 rad/s ) 15 ft/s at = rα = = 1 a n 6 = rω = ft (0 rad/s) = 00 ft/s 1 W 1 lb m = = = lb s /ft g 3. ft/s Kinetics. m 10 0 I = ( lb s /ft)( ft ) lb s ft 1 + = = 1 1 (a) Force P. Σ MA =Σ( MA) : P ft W ft mat ft Iα 1 = P = (1) (0.3767)(15) ( )(30) P = 9.04 lb. P = 9.0 lb PROPRIETARY MATERIAL. 013 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual ma be displaed, 1537

11 PROBLEM (Continued) (b) Reaction at A. 1 Σ F =Σ ( F) : A = man = (00) 3. A = lb A 74.5 lb = Σ F =Σ ( F ) : A + P W = ma t 1 A = W + mat P= 1 + (15) 9.0 = 8.57 lb 3. A = 8.57 lb PROPRIETARY MATERIAL. 013 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual ma be displaed, 1538

12 PROBLEM A drum of 60-mm radius is attached to a disk of 10-mm radius. The disk and drum have a total mass of 6 kg and a combined radius of gration of 90 mm. A cord is attached as shown and pulled with a force P of magnitude 0 N. Knowing that the disk rolls without sliding, determine (a) the angular acceleration of the disk and the acceleration of G, (b) the minimum value of the coicient of static friction compatible with this motion. (a) (b) a = rα = (0.1 m) α I = mk = (6 kg)(0.09 m) I = kg m Σ M =Σ ( M ) : (0 N)(0.1 m) = ( ma) r + Iα C C Σ F =Σ ( F ) : N mg = 0 Σ F =Σ( F ) : 0 N F = ma 3 3.4N m = (6kg)(0.1m) α kg m 3.4 = α α = rad/s a = rα = (0.1 m)( rad/s ) =.133 m/s N = (6 kg)(9.81 m/s ) N = N 0 N F = (6 kg)(.133 m/s ) F = 7.0 N α = rad/s a =.13 m/s ( ) F N 7.0 N N μ s min = = s min ( μ ) = 0.1 PROPRIETARY MATERIAL. 013 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual ma be displaed, 1558

13 PROBLEM The ends of the 0-lb uniform rod AB are attached to collars of negligible mass that slide without friction along fied rods. If the rod is released from rest when θ = 5, determine immediatel after release (a) the angular acceleration of the rod, (b) the reaction at A, (c) the reaction at B. Kinematics: Assume α ω = 0 a = a + a / = [ a ] + [4α 5 ] B A B A A a = (4 α)cos 5 = 3.65α B a = (4 α)sin 5 = α A a a a ] + [α 5 ] G = A + G/ A = [ aa a = [1.6905α ] + [α 5 ] G a = ( a ) = [1.6905α ] + [0.8454α ] a G a = α We have found for α a = α Kinetics: a = [α cos5 ] = 1.816α = 1.816α 1 1 I = ml = m(4 ft) 1 1 PROPRIETARY MATERIAL. 013 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual ma be displaed, 1588

14 PROBLEM (Continued) (a) Angular acceleration. Σ M =Σ ( M ) : mg(1.816 ft) = Iα + ma ( ft) + ma (1.816 ft) E E 1 mg(1.816) = m(4) α + m(0.8454) α + m(1.816) α 1 g(1.816) = α α = g α = rad/s (b) Σ F =Σ( F ) : A mg = ma = m(1.816 α) 0 A 0 = (1.816)(10.944) 3. A = = lb A = 7.68 lb (c) Σ F =Σ ( F ) : B= ma = m( α) 0 B = (0.8454)(10.944) 3. B = lb B = 5.75 lb PROPRIETARY MATERIAL. 013 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual ma be displaed, 1589

15 PROBLEM The 7-lb uniform rod AB is connected to crank BD and to a collar of negligible weight, which can slide freel along rod EF. Knowing that in the position shown crank BD rotates with an angular velocit of 15 rad/s and an angular acceleration of 60 rad/s, both clockwise, determine the reaction at A. Crank BD: ω α BD BD 4 = 15 rad/s, vb = ft (15 rad/s) = 5 ft/s 1 = 60 rad/s 4 ( a B) = ft (60 rad/s ) = 0 ft/s 1 4 ( a B) = ft (15rad/s) = 75ft/s 1 Rod AB: Velocit: Instantaneous center at C. Acceleration: CB 5 = ft / tan 30 = ft 1 ω AB vb 5ft/s = = = rad/s CB ft 5 ( a ) = ( AB) α = α 1 AB / t AB AB 5 ( a ) ( ) (1.3856) 4 ft/s 1 AB / n = AB ωab = = ( a ) = ( GB) α G/ B t AB 1.5 = α AB 1 PROPRIETARY MATERIAL. 013 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual ma be displaed, 160

16 PROBLEM (Continued) ( a GB / ) n 1.5 = ( GB) ω AB = (1.3856) = ft/s 1 a = a + a = a + ( a ) + ( a ) A B B/ A B B/ A t G/ A n [ a A 30 ] = [0 ] + [75 5 ] + α 1 AB + [4 a cos30 = 0 4; a = ft/s 30 A 5 (18.475)sin 30 = 75 α AB; α AB = rad/s 1 a = a + a = a + ( a ) + ( a ) B G/ B B G/ B t G/ B n a = [0 ] [ a = 0 = 18; a = 18 ft/s A ] + [ (31.566) ] + [ ] a = = 4.119; a = ft/s ] Kinetics: I 1 7lb 5 = m( AB) = ft slug ft 1 1(3.) = Σ MB =Σ ( MB) : ( Asin 60 ) ft mg ft Iα AB ma ft 1 = A (7 lb) ft = ( slug ft )( rad/s ) + slug (4.119 ft/s ) ft A = A = 7.95 lb A = 7.95 lb 60 PROPRIETARY MATERIAL. 013 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual ma be displaed, 1603

17 PROBLEM Two 8-lb uniform bars are connected to form the linkage shown. Neglecting the ect of friction, determine the reaction at D immediatel after the linkage is released from rest in the position shown. Kinematics: Bar AC: Rotation about C 15 a = ( BC) α = ft α 1 Bar BC: a / a =1.5α 15 in. sinθ = θ = in. DB = Lα Must be zero since a D α BD = 0 and abd = a Kinetics: Bar BD Σ F =Σ( F ) : B W = ma B 8lb 8lb = (1.5 α) 3. B = α (1) PROPRIETARY MATERIAL. 013 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual ma be displaed, 161

18 PROBLEM (Continued) Σ M =Σ( M ) : D(.165 ft) W(0.65 ft) = ma(0.65 ft) B B Bar AC: 8lb D(.165 ft) (8 lb)(0.65 ft) = (1.5 α)(0.65 ft) 3. D = α () 1 I = m( AC) lb (.5 ft) = 1 3. = lb ft s Substitute from Eq. (1) for Σ M =Σ ( M ) : W(1.5 ft) + B (1.5 ft) = Iα + m(1.5 α)(1.5) C C B 8 8(1.5) + ( α)(1.5) = (0.194) α + (1.5) α α = 0.194α α 0 = α α =.08 rad/s Eq. (), D = α = (.08) = D = lb D = lb PROPRIETARY MATERIAL. 013 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual ma be displaed, 16

+ ] B A BA / t BA / n. B G BG / t BG / n. a = (5)(4) = 80 in./s. A G AG / t AG / n. ] + [48 in./s ]

+ ] B A BA / t BA / n. B G BG / t BG / n. a = (5)(4) = 80 in./s. A G AG / t AG / n. ] + [48 in./s ] PROLEM 15.113 3-in.-radius drum is rigidly attached to a 5-in.-radius drum as shown. One of the drums rolls without sliding on the surface shown, and a cord is wound around the other drum. Knowing that

More information

PROBLEM rad/s r. v = ft/s

PROBLEM rad/s r. v = ft/s PROLEM 15.38 An automobile traels to the right at a constant speed of 48 mi/h. If the diameter of a wheel is 22 in., determine the elocities of Points, C,, and E on the rim of the wheel. A 48 mi/h 70.4

More information

DYNAMICS VECTOR MECHANICS FOR ENGINEERS: Plane Motion of Rigid Bodies: Energy and Momentum Methods. Seventh Edition CHAPTER

DYNAMICS VECTOR MECHANICS FOR ENGINEERS: Plane Motion of Rigid Bodies: Energy and Momentum Methods. Seventh Edition CHAPTER CHAPTER 7 VECTOR MECHANICS FOR ENGINEERS: DYNAMICS Ferdinand P. Beer E. Russell Johnston, Jr. Lecture Notes: J. Walt Oler Texas Tech University Plane Motion of Rigid Bodies: Energy and Momentum Methods

More information

Problems. B 60 mm. 80 mm. 80 mm. 120 mm

Problems. 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 information

Plane Motion of Rigid Bodies: Forces and Accelerations

Plane 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 information

Dynamics Plane kinematics of rigid bodies Section 4: TJW Rotation: Example 1

Dynamics 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 information

The University of Melbourne Engineering Mechanics

The University of Melbourne Engineering Mechanics The University of Melbourne 436-291 Engineering Mechanics Tutorial Eleven Instantaneous Centre and General Motion Part A (Introductory) 1. (Problem 5/93 from Meriam and Kraige - Dynamics) For the instant

More information

5. Plane Kinetics of Rigid Bodies

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 information

PROBLEM Copyright McGraw-Hill Education. Permission required for reproduction or display. SOLUTION

PROBLEM Copyright McGraw-Hill Education. Permission required for reproduction or display. SOLUTION PROLEM 7. The rotor of an electric motor has an angular velocity of 600 rpm when the load and power are cut off. The 0-lb rotor, which has a centroidal radius of gyration of 9 in., then coasts to rest.

More information

Physics 2210 Homework 18 Spring 2015

Physics 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 information

CEE 271: Applied Mechanics II, Dynamics Lecture 25: Ch.17, Sec.4-5

CEE 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 information

Since the cylinder rolls without slipping, the point of contact with the ground is the instantaneous center. r Ë Á 1 2ˆ = = = r

Since the cylinder rolls without slipping, the point of contact with the ground is the instantaneous center. r Ë Á 1 2ˆ = = = r PROBEM 7.7 A 0-kg uniform cylindrical roller, initially at rest, is acted upon by a 90-N force as shown. Knowing that the body rolls without slipping, determine (a) the velocity of its center G after it

More information

Problem 1 Problem 2 Problem 3 Problem 4 Total

Problem 1 Problem 2 Problem 3 Problem 4 Total Name Section THE PENNSYLVANIA STATE UNIVERSITY Department of Engineering Science and Mechanics Engineering Mechanics 12 Final Exam May 5, 2003 8:00 9:50 am (110 minutes) Problem 1 Problem 2 Problem 3 Problem

More information

Rotation. PHYS 101 Previous Exam Problems CHAPTER

Rotation. 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 information

UNIVERSITY OF SASKATCHEWAN GE MECHANICS III FINAL EXAM APRIL 18, 2011 Professor A. Dolovich A CLOSED BOOK EXAMINATION TIME: 3 HOURS

UNIVERSITY 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 information

6. Find the net torque on the wheel in Figure about the axle through O if a = 10.0 cm and b = 25.0 cm.

6. Find the net torque on the wheel in Figure about the axle through O if a = 10.0 cm and b = 25.0 cm. 1. During a certain period of time, the angular position of a swinging door is described by θ = 5.00 + 10.0t + 2.00t 2, where θ is in radians and t is in seconds. Determine the angular position, angular

More information

SOLUTION 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.

SOLUTION 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 information

is acting on a body of mass m = 3.0 kg and changes its velocity from an initial

is acting on a body of mass m = 3.0 kg and changes its velocity from an initial PHYS 101 second major Exam Term 102 (Zero Version) Q1. A 15.0-kg block is pulled over a rough, horizontal surface by a constant force of 70.0 N acting at an angle of 20.0 above the horizontal. The block

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 information

AP Physics. Harmonic Motion. Multiple Choice. Test E

AP Physics. Harmonic Motion. Multiple Choice. Test E AP Physics Harmonic Motion Multiple Choice Test E A 0.10-Kg 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 information

Kinematics, Dynamics, and Vibrations FE Review Session. Dr. David Herrin March 27, 2012

Kinematics, 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 information

A Ferris wheel in Japan has a radius of 50m and a mass of 1.2 x 10 6 kg. If a torque of 1 x 10 9 Nm is needed to turn the wheel when it starts at

A Ferris wheel in Japan has a radius of 50m and a mass of 1.2 x 10 6 kg. If a torque of 1 x 10 9 Nm is needed to turn the wheel when it starts at Option B Quiz 1. A Ferris wheel in Japan has a radius of 50m and a mass of 1. x 10 6 kg. If a torque of 1 x 10 9 Nm is needed to turn the wheel when it starts at rest, what is the wheel s angular acceleration?

More information

DYNAMICS VECTOR MECHANICS FOR ENGINEERS: Plane Motion of Rigid Bodies: Energy and Momentum Methods. Tenth Edition CHAPTER

DYNAMICS VECTOR MECHANICS FOR ENGINEERS: Plane Motion of Rigid Bodies: Energy and Momentum Methods. Tenth Edition CHAPTER Tenth E CHAPTER 7 VECTOR MECHANICS FOR ENGINEERS: DYNAMICS Ferdinand P. Beer E. Russell Johnston, Jr. Phillip J. Cornwell Lecture Notes: Brian P. Self California State Polytechnic University Plane Motion

More information

7.6 Journal Bearings

7.6 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 information

Rotational Motion. Rotational Motion. Rotational Motion

Rotational 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 information

Physics 4A Solutions to Chapter 10 Homework

Physics 4A Solutions to Chapter 10 Homework Physics 4A Solutions to Chapter 0 Homework Chapter 0 Questions: 4, 6, 8 Exercises & Problems 6, 3, 6, 4, 45, 5, 5, 7, 8 Answers to Questions: Q 0-4 (a) positive (b) zero (c) negative (d) negative Q 0-6

More information

DYNAMICS ME HOMEWORK PROBLEM SETS

DYNAMICS 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 information

Angular velocity and angular acceleration CHAPTER 9 ROTATION. Angular velocity and angular acceleration. ! equations of rotational motion

Angular 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 information

Phys101 Second Major-173 Zero Version Coordinator: Dr. M. Al-Kuhaili Thursday, August 02, 2018 Page: 1. = 159 kw

Phys101 Second Major-173 Zero Version Coordinator: Dr. M. Al-Kuhaili Thursday, August 02, 2018 Page: 1. = 159 kw Coordinator: Dr. M. Al-Kuhaili Thursday, August 2, 218 Page: 1 Q1. A car, of mass 23 kg, reaches a speed of 29. m/s in 6.1 s starting from rest. What is the average power used by the engine during the

More information

Moving Reference Frame Kinematics Homework

Moving Reference Frame Kinematics Homework Chapter 3 Moving Reference Frame Kinematics Homework Freeform c 2016 3-1 3-2 Freeform c 2016 Homework 3. Given: n L-shaped telescoping arm is pinned to ground at point. The arm is rotating counterclockwise

More information

Chapter 8 Lecture Notes

Chapter 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 information

16.07 Dynamics Final Exam

16.07 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 information

Final Exam April 30, 2013

Final 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

Exam 3 Practice Solutions

Exam 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 information

5/2/2015 7:42 AM. Chapter 17. Plane Motion of Rigid Bodies: Energy and Momentum Methods. Mohammad Suliman Abuhaiba, Ph.D., PE

5/2/2015 7:42 AM. Chapter 17. Plane Motion of Rigid Bodies: Energy and Momentum Methods. Mohammad Suliman Abuhaiba, Ph.D., PE 5//05 7:4 AM Chapter 7 Plane Motion of Rigid Bodies: Energy and Momentum Methods 5//05 7:4 AM Chapter Outline Principle of Work and Energy for a Rigid Body Work of Forces Acting on a Rigid Body Kinetic

More information

ENGR 3311: DYNAMICS SPRING 2018

ENGR 3311: DYNAMICS SPRING 2018 NAME: Exam 03: Chapters 16 and 17 INSTRUCTIONS Solve each of the following problems to the best of your ability. Read and follow the directions carefully. Solve using the method required by the problem

More information

Dynamics of Rotation

Dynamics 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 information

Problem Set x Classical Mechanics, Fall 2016 Massachusetts Institute of Technology. 1. Moment of Inertia: Disc and Washer

Problem 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 information

Chapter 10 Practice Test

Chapter 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 information

In this chapter the energy and momentum methods will be added to the tools available for your study of the motion of rigid bodies.

In this chapter the energy and momentum methods will be added to the tools available for your study of the motion of rigid bodies. In this chapter the energy and momentum methods will be added to the tools available for your study of the motion of rigid bodies. For example, by using the principle of conservation of energy and direct

More information

1 MR SAMPLE EXAM 3 FALL 2013

1 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 information

PLANAR KINETIC EQUATIONS OF MOTION: TRANSLATION

PLANAR 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 information

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.

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. 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. In-Class Activities: 2. Apply the principle of work

More information

Physics 125, Spring 2006 Monday, May 15, 8:00-10:30am, Old Chem 116. R01 Mon. 12:50 R02 Wed. 12:50 R03 Mon. 3:50. Final Exam

Physics 125, Spring 2006 Monday, May 15, 8:00-10:30am, Old Chem 116. R01 Mon. 12:50 R02 Wed. 12:50 R03 Mon. 3:50. Final Exam Monday, May 15, 8:00-10:30am, Old Chem 116 Name: Recitation section (circle one) R01 Mon. 12:50 R02 Wed. 12:50 R03 Mon. 3:50 Closed book. No notes allowed. Any calculators are permitted. There are no trick

More information

1. 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.

1. 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

Force and Moment. Figure 1 Figure 2

Force 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 information

Class XI Chapter 7- System of Particles and Rotational Motion Physics

Class XI Chapter 7- System of Particles and Rotational Motion Physics Page 178 Question 7.1: Give the location of the centre of mass of a (i) sphere, (ii) cylinder, (iii) ring, and (iv) cube, each of uniform mass density. Does the centre of mass of a body necessarily lie

More information

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

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 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 information

TUTORIAL SHEET 1. magnitude of P and the values of ø and θ. Ans: ø =74 0 and θ= 53 0

TUTORIAL 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 information

11-2 A General Method, and Rolling without Slipping

11-2 A General Method, and Rolling without Slipping 11-2 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

31 ROTATIONAL KINEMATICS

31 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 information

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

We 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 information

PHYSICS 221, FALL 2011 EXAM #2 SOLUTIONS WEDNESDAY, NOVEMBER 2, 2011

PHYSICS 221, FALL 2011 EXAM #2 SOLUTIONS WEDNESDAY, NOVEMBER 2, 2011 PHYSICS 1, FALL 011 EXAM SOLUTIONS WEDNESDAY, NOVEMBER, 011 Note: The unit vectors in the +x, +y, and +z directions of a right-handed Cartesian coordinate system are î, ĵ, and ˆk, respectively. In this

More information

Three-bladed wind turbines, similar to the ones shown in this picture of a wind farm, are currently the most common design. In this chapter you will

Three-bladed wind turbines, similar to the ones shown in this picture of a wind farm, are currently the most common design. In this chapter you will Three-bladed wind turbines, similar to the ones shown in this picture of a wind farm, are currently the most common design. In this chapter you will learn to analyze the motion of a rigid body by considering

More information

Chapters 10 & 11: Rotational Dynamics Thursday March 8 th

Chapters 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 information

Physics 201 Exam 3 (Monday, November 5) Fall 2012 (Saslow)

Physics 201 Exam 3 (Monday, November 5) Fall 2012 (Saslow) Physics 201 Exam 3 (Monday, November 5) Fall 2012 (Saslow) Name (printed) Lab Section(+2 pts) Name (signed as on ID) Multiple choice Section. Circle the correct answer. No work need be shown and no partial

More information

Circular Motion, Pt 2: Angular Dynamics. Mr. Velazquez AP/Honors Physics

Circular 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 information

E 490 FE Exam Prep. Engineering Mechanics

E 490 FE Exam Prep. Engineering Mechanics E 490 FE Exam Prep Engineering Mechanics 2008 E 490 Course Topics Statics Newton s Laws of Motion Resultant Force Systems Moment of Forces and Couples Equilibrium Pulley Systems Trusses Centroid of an

More information

PLANAR KINETIC EQUATIONS OF MOTION: TRANSLATION

PLANAR 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 information

Rotational Motion and Torque

Rotational Motion and Torque Rotational Motion and Torque Introduction to Angular Quantities Sections 8- to 8-2 Introduction Rotational motion deals with spinning objects, or objects rotating around some point. Rotational motion is

More information

Chapter 10. Rotation

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 MFMcGraw-PHY 45 Chap_10Ha-Rotation-Revised

More information

I xx + I yy + I zz = (y 2 + z 2 )dm + (x 2 + y 2 )dm. (x 2 + z 2 )dm + (x 2 + y 2 + z 2 )dm = 2

I xx + I yy + I zz = (y 2 + z 2 )dm + (x 2 + y 2 )dm. (x 2 + z 2 )dm + (x 2 + y 2 + z 2 )dm = 2 9196_1_s1_p095-0987 6/8/09 1:09 PM Page 95 010 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This material is protected under all copright laws as the currentl 1 1. Show that the

More information

CEE 271: Applied Mechanics II, Dynamics Lecture 27: Ch.18, Sec.1 5

CEE 271: Applied Mechanics II, Dynamics Lecture 27: Ch.18, Sec.1 5 1 / 42 CEE 271: Applied Mechanics II, Dynamics Lecture 27: Ch.18, Sec.1 5 Prof. Albert S. Kim Civil and Environmental Engineering, University of Hawaii at Manoa Tuesday, November 27, 2012 2 / 42 KINETIC

More information

AP Physics C: Rotation II. (Torque and Rotational Dynamics, Rolling Motion) Problems

AP 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 information

ME 274 Spring 2017 Examination No. 2 PROBLEM No. 2 (20 pts.) Given:

ME 274 Spring 2017 Examination No. 2 PROBLEM No. 2 (20 pts.) Given: PROBLEM No. 2 (20 pts.) Given: Blocks A and B (having masses of 2m and m, respectively) are connected by an inextensible cable, with the cable being pulled over a small pulley of negligible mass. Block

More information

VALLIAMMAI ENGINEERING COLLEGE SRM NAGAR, KATTANKULATHUR DEPARTMENT OF MECHANICAL ENGINEERING

VALLIAMMAI 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 information

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

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 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 information

AP Physics 1: Rotational Motion & Dynamics: Problem Set

AP Physics 1: Rotational Motion & Dynamics: Problem Set AP Physics 1: Rotational Motion & Dynamics: Problem Set I. Axis of Rotation and Angular Properties 1. How many radians are subtended by a 0.10 m arc of a circle of radius 0.40 m? 2. How many degrees are

More information

MET 327 APPLIED ENGINEERING II (DYNAMICS) 1-D Dynamic System Equation of Motion (EOM)

MET 327 APPLIED ENGINEERING II (DYNAMICS) 1-D Dynamic System Equation of Motion (EOM) Handout #1 by Hejie Lin MET 327 APPLIED ENGINEERING II (DYNAMICS) 1. Introduction to Statics and Dynamics 1.1 Statics vs. Dynamics 1 Ch 9 Moment of Inertia A dynamic system is characterized with mass (M),

More information

Webreview Torque and Rotation Practice Test

Webreview 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 information

Solution 11. Kinetics of rigid body(newton s Second Law)

Solution 11. Kinetics of rigid body(newton s Second Law) Solution () urpose and Requirement Solution Kinetics of rigid bod(newton s Second Law) In rob, kinematics stud regarding acceleration of mass center should be done before Newton s second law is used to

More information

C7047. PART A Answer all questions, each carries 5 marks.

C7047. PART A Answer all questions, each carries 5 marks. 7047 Reg No.: Total Pages: 3 Name: Max. Marks: 100 PJ DUL KLM TEHNOLOGIL UNIVERSITY FIRST SEMESTER.TEH DEGREE EXMINTION, DEEMER 2017 ourse ode: E100 ourse Name: ENGINEERING MEHNIS PRT nswer all questions,

More information

Dept of ECE, SCMS Cochin

Dept of ECE, SCMS Cochin B B2B109 Pages: 3 Reg. No. Name: APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY SECOND SEMESTER B.TECH DEGREE EXAMINATION, MAY 2017 Course Code: BE 100 Course Name: ENGINEERING MECHANICS Max. Marks: 100 Duration:

More information

Suggested Problems. Chapter 1

Suggested 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 information

Chapter 10 Rotational Kinematics and Energy. Copyright 2010 Pearson Education, Inc.

Chapter 10 Rotational Kinematics and Energy. Copyright 2010 Pearson Education, Inc. Chapter 10 Rotational Kinematics and Energy Copyright 010 Pearson Education, Inc. 10-1 Angular Position, Velocity, and Acceleration Copyright 010 Pearson Education, Inc. 10-1 Angular Position, Velocity,

More information

Write your name legibly on the top right hand corner of this paper

Write your name legibly on the top right hand corner of this paper NAME Phys 631 Summer 2007 Quiz 2 Tuesday July 24, 2007 Instructor R. A. Lindgren 9:00 am 12:00 am Write your name legibly on the top right hand corner of this paper No Books or Notes allowed Calculator

More information

PLANAR RIGID BODY MOTION: TRANSLATION &

PLANAR 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 information

Torque. Physics 6A. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

Torque. Physics 6A. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Physics 6A Torque is what causes angular acceleration (just like a force causes linear acceleration) Torque is what causes angular acceleration (just like a force causes linear acceleration) For a torque

More information

JNTU World. Subject Code: R13110/R13

JNTU World. Subject Code: R13110/R13 Set No - 1 I B. Tech I Semester Regular Examinations Feb./Mar. - 2014 ENGINEERING MECHANICS (Common to CE, ME, CSE, PCE, IT, Chem E, Aero E, AME, Min E, PE, Metal E) Time: 3 hours Max. Marks: 70 Question

More information

Name: Date: Period: AP Physics C Rotational Motion HO19

Name: 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 information

UNIVERSITI TUN HUSSEIN ONN MALAYSIA FINAL EXAMINATION SEMESTER I SESSION 2009/2010

UNIVERSITI 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 information

General Physics 1. School of Science, University of Tehran Fall Exercises (set 07)

General Physics 1. School of Science, University of Tehran Fall Exercises (set 07) General Physics 1 School of Science, University of Tehran Fall 1396-97 Exercises (set 07) 1. In Fig., wheel A of radius r A 10cm is coupled by belt B to wheel C of radius r C 25 cm. The angular speed of

More information

ME Machine Design I. EXAM 1. OPEN BOOK AND CLOSED NOTES. Wednesday, September 30th, 2009

ME Machine Design I. EXAM 1. OPEN BOOK AND CLOSED NOTES. Wednesday, September 30th, 2009 ME - Machine Design I Fall Semester 009 Name Lab. Div. EXAM. OPEN BOOK AND CLOSED NOTES. Wednesday, September 0th, 009 Please use the blank paper provided for your solutions. Write on one side of the paper

More information

Pleeeeeeeeeeeeeease mark your UFID, exam number, and name correctly. 20 problems 3 problems from exam 2

Pleeeeeeeeeeeeeease mark your UFID, exam number, and name correctly. 20 problems 3 problems from exam 2 Pleeeeeeeeeeeeeease mark your UFID, exam number, and name correctly. 20 problems 3 problems from exam 1 3 problems from exam 2 6 problems 13.1 14.6 (including 14.5) 8 problems 1.1---9.6 Go through the

More information

Chapter 9. Rotational Dynamics

Chapter 9. Rotational Dynamics Chapter 9 Rotational Dynamics In pure translational motion, all points on an object travel on parallel paths. The most general motion is a combination of translation and rotation. 1) Torque Produces angular

More information

Chapter 8: Momentum, Impulse, & Collisions. Newton s second law in terms of momentum:

Chapter 8: Momentum, Impulse, & Collisions. Newton s second law in terms of momentum: linear momentum: Chapter 8: Momentum, Impulse, & Collisions Newton s second law in terms of momentum: impulse: Under what SPECIFIC condition is linear momentum conserved? (The answer does not involve collisions.)

More information

Name (please print): UW ID# score last first

Name (please print): UW ID# score last first Name (please print): UW ID# score last first Question I. (20 pts) Projectile motion A ball of mass 0.3 kg is thrown at an angle of 30 o above the horizontal. Ignore air resistance. It hits the ground 100

More information

PROBLEMS ON EQUILIBRIUM OF PARTICLES

PROBLEMS ON EQUILIBRIUM OF PARTICLES O EQUILIBRIUM O PRICLES 1. ind the angle of tilt q with the horiontal so that the contact force at B will be one-half that at for the smooth clinder. (3/15) q?, contact force at B will be one-half that

More information

AP Physics Multiple Choice Practice Torque

AP Physics Multiple Choice Practice Torque AP Physics Multiple Choice Practice Torque 1. A uniform meterstick of mass 0.20 kg is pivoted at the 40 cm mark. Where should one hang a mass of 0.50 kg to balance the stick? (A) 16 cm (B) 36 cm (C) 44

More information

Rigid Body Kinetics :: Force/Mass/Acc

Rigid Body Kinetics :: Force/Mass/Acc Rigid Body Kinetics :: Force/Mass/Acc General Equations of Motion G is the mass center of the body Action Dynamic Response 1 Rigid Body Kinetics :: Force/Mass/Acc Fixed Axis Rotation All points in body

More information

Name Date Period PROBLEM SET: ROTATIONAL DYNAMICS

Name 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 information

Exam 02: Chapters 16 19

Exam 02: Chapters 16 19 NAME: Exam 02: Chapters 16 19 Instructions Solve six of the following problems to the best of your ability. You have two hours in which to complete this exam. Choose one problem from each chapter, then

More information

A) 4.0 m/s B) 5.0 m/s C) 0 m/s D) 3.0 m/s E) 2.0 m/s. Ans: Q2.

A) 4.0 m/s B) 5.0 m/s C) 0 m/s D) 3.0 m/s E) 2.0 m/s. Ans: Q2. Coordinator: Dr. W. Al-Basheer Thursday, July 30, 2015 Page: 1 Q1. A constant force F ( 7.0ˆ i 2.0 ˆj ) N acts on a 2.0 kg block, initially at rest, on a frictionless horizontal surface. If the force causes

More information

SOLUTION 8 1. a+ M B = 0; N A = 0. N A = kn = 16.5 kn. Ans. + c F y = 0; N B = 0

SOLUTION 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 information

PROBLEM Copyright McGraw-Hill Education. Permission required for reproduction or display. SOLUTION

PROBLEM Copyright McGraw-Hill Education. Permission required for reproduction or display. SOLUTION PROLEM 15.10 The bent rod E rotates about a line joining Points and E with a constant angular elocity of 9 rad/s. Knowing that the rotation is clockwise as iewed from E, determine the elocity and acceleration

More information

AP Physics 1- Torque, Rotational Inertia, and Angular Momentum Practice Problems FACT: The center of mass of a system of objects obeys Newton s second law- F = Ma cm. Usually the location of the center

More information

Lecture Outline Chapter 10. Physics, 4 th Edition James S. Walker. Copyright 2010 Pearson Education, Inc.

Lecture Outline Chapter 10. Physics, 4 th Edition James S. Walker. Copyright 2010 Pearson Education, Inc. Lecture Outline Chapter 10 Physics, 4 th Edition James S. Walker Chapter 10 Rotational Kinematics and Energy Units of Chapter 10 Angular Position, Velocity, and Acceleration Rotational Kinematics Connections

More information

SOLUTION 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,

SOLUTION 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 information

Rotational Dynamics Smart Pulley

Rotational Dynamics Smart Pulley Rotational Dynamics Smart Pulley The motion of the flywheel of a steam engine, an airplane propeller, and any rotating wheel are examples of a very important type of motion called rotational motion. If

More information

CHAPTER 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 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 information