Mekanika Teknik

Chapter 1: Statics

1. The subject of mechanics deals with what happens to a body when ______ is / are applied to it.

A) magnetic field B) heat C ) forces D) neutrons E) lasers

2. ________________ still remains the basis of most of today’s engineering sciences.

A) Newtonian Mechanics B) Relativistic Mechanics

C) Greek Mechanics C) Euclidean Mechanics

3. For a statics problem your calculations show the final answer as 12345.6 N. What will you write as your final answer?

A) 12345.6 N

B) 12.3456 kN

C) 12 kN

D) 12.3 kN

E) 123 kN

4. In three step IPE approach to problem solving, what does P stand for?

A) Position

B) Plan

C) Problem

D) Practical

E) Possible

Chapter 2: Statics

1. The dot product of two vectors P and Q is defined as

A) P Q cos θ B) P Q sin θ C) P Q tan θ D) P Q sec θ

2. The dot product of two vectors results in a _________ quantity.

A ) Scalar B) Vector C) Complex D) Zero

3. If a dot product of two non-‐zero vectors is 0, then the two vectors must be _____________ to each other.

A) Parallel (pointing in the same direction)

B) Parallel (pointing in the opposite direction)

C) Perpendicular

D) Cannot be determined.

4. If a dot product of two non-‐zero vectors equals -‐1, then the vectors must be ________ to each other.

A) Parallel (pointing in the same direction)

B) Parallel (pointing in the opposite direction)

C) Perpendicular D) Cannot be determined.

5. The dot product can be used to find all of the following except ____ .

A) sum of two vectors B) angle between two vectors

C) component of a vector parallel to another line

D) component of a vector perpendicular to another line

6. Find the dot product of the two vectors P and Q.

P = {5 i + 2 j + 3 k} m and Q = {-‐2 i + 5 j + 4 k} m

A) -‐12 m B) 12 m C) 12 m 2 D) -‐12 m 2 E) 10 m 2

Chapter 2 (Cont.): Statics 1. Which one of the following is a scalar quantity?

A) Force B) Position C) Mass D) Velocity 2. For vector addition, you have to use ______ law. A) Newton’s Second B) the arithmetic C) Pascal’s D) the parallelogram 3. Can you resolve a 2-‐D vector along two directions, which are not at 90° to each other? A) Yes, but not uniquely. B) No. C) Yes, uniquely. 4. Can you resolve a 2-‐D vector along three directions (say at 0, 60, and 120°)? A) Yes, but not uniquely. B) No. C) Yes, uniquely. 5. Resolve F along x and y axes and write it in vector form, for θ=30 o, F = { ___________ } N A) 80 cos (30°) i – 80 sin (30°) j B) 80 sin (30°) i + 80 cos (30°) j C) 80 sin (30°) i – 80 cos (30°) j D) 80 cos (30°) i + 80 sin (30°) j 6. Determine the magnitude of the resultant (F1 + F2) force in N , when F1 = { 10 i + 20 j } N and F2 = { 20 i + 20 j } N .

A) 30 N B) 40 N C) 50 N D) 60 N E) 70 N 7. Vector algebra, as we are going to use it, is based on a ___________ coordinate system. A) Euclidean B) Left-‐handed C) Greek D) Right-‐handed E) Egyptian

y x

θ F=80 N

8. The symbols α, β, and γ designate the __________ of a 3-‐D Cartesian vector. A) Unit vectors B) Coordinate direction angles C) Greek societies D) X, Y and Z components 9. If you know only uA, you can determine the ________ of A uniquely. A) magnitude B) angles (α, β and γ) C) components (AX, AY, & AZ) D) All of the above. 10. For a force vector, the following parameters are randomly generated. The magnitude is 0.9 N, α= 30º , β= 70º , γ = 100º. What is wrong with this 3-‐D vector ? A) Magnitude is too small. B) Angles are too large. C) All three angles are arbitrarily picked. D) All three angles are between 0º to 180º. 11. What is not true about an unit vector, uA ? A) It is dimensionless. B) Its magnitude is one. C) It always points in the direction of positive X-‐ axis. D) It always points in the direction of vector A. 12. If F = {10 i + 10 j + 10 k} N and G = {20 i + 20 j + 20 k } N, then F + G = { ____ } N A) 10 i + 10 j + 10 k B) 30 i + 20 j + 30 k C) – 10 i – 10 j – 10 k D) 30 i + 30 j + 30 k 13. A position vector, rPQ, is obtained by A) Coordinates of Q minus coordinates of P B) Coordinates of P minus coordinates of Q C) Coordinates of Q minus coordinates of the origin D) Coordinates of the origin minus coordinates of P 14. A force of magnitude F, directed along a unit vector U, is given by F = ______ . A) F (U) B) U / F C) F / U D) F + U E) F – U

15. P and Q are two points in a 3-‐D space. How are the position vectors rPQ and rQP related? A) rPQ = rQP B) rPQ = -‐ rQP C) rPQ = 1/rQP D) rPQ = 2 rQP 16. If F and r are force vector and position vectors, respectively, in SI units, what are the units of the expression (r * (F / F)) ? A) Newton B) Dimensionless C) Meter D) Newton -‐ Meter E) The expression is algebraically illegal. 17. Two points in 3 – D space have coordinates of P (1, 2, 3) and Q (4, 5, 6) meters. The position vector rQP is given by A) {3 i + 3 j + 3 k} m B) {– 3 i – 3 j – 3 k} m C) {5 i + 7 j + 9 k} m D) {– 3 i + 3 j + 3 k} m E) {4 i + 5 j + 6 k} m 18. Force vector, F, directed along a line PQ is given by A) (F/ F) rPQ B) rPQ/rPQ C) F(rPQ/rPQ) D) F(rPQ/rPQ)

Chapter 3. Statics 1. Particle P is in equilibrium with five (5) forces acting on it in 3-‐D space. How many scalar equations of equilibrium can be written for point P? A) 2 B) 3 C) 4 D) 5 E) 6 2. In 3-‐D, when a particle is in equilibrium, which of the following equations apply?

A) (Σ Fx) i + (Σ Fy) j + (Σ Fz) k = 0 B) Σ F = 0 C) Σ Fx = Σ Fy = Σ Fz = 0 D) All of the above. E) None of the above.

3. In 3-‐D, when you know the direction of a force but not its magnitude, how many unknowns corresponding to that force remain? A) One B) Two C) Three D) Four 4. If a particle has 3-‐D forces acting on it and is in static equilibrium, the components of the resultant force (Σ Fx, Σ Fy, and Σ Fz ) ___ . A) have to sum to zero, e.g., -‐5 i + 3 j + 2 k B) have to equal zero, e.g., 0 i + 0 j + 0 k C) have to be positive, e.g., 5 i + 5 j + 5 k D) have to be negative, e.g., -‐5 i -‐ 5 j -‐ 5 k 5. In 3-‐D, when you don’t know the direction or the magnitude of a force, how many unknowns do you have corresponding to that force? A) One B) Two C) Three D) Four 6. When a particle is in equilibrium, the sum of forces acting on it equals ___ . (Choose the most appropriate answer) A) A constant B) A positive number C) Zero D) A negative number E) An integer 7. For a frictionless pulley and cable, tensions in the cable (T1 and T2) are related as _____ . A) T1 > T2 B) T1 = T2 C) T1 < T2 D) T1 = T2 sin θ

8. Assuming you know the geometry of the ropes, you cannot determine the forces in the cables in which system below? A, B, or C ? A) B) C)

9. Why?

A) The weight is too heavy. B) The cables are too thin. C) There are more unknowns than equations. D) There are too few cables for a 1000 lb weight. 10.

The correct answer is: (D)

11. The correct answer is: (B)

Chapter 4. Statics 1. When determining the moment of a force about a specified axis, the axis must be along _____________. A) the x axis B) the y axis C) the z axis D) any line in 3-‐D space E) any line in the x-‐y plane 2. The triple scalar product u • ( r × F ) results in A) a scalar quantity ( + or -‐ ). B) a vector quantity. C) zero. D) a unit vector. E) an imaginary number. 3. The vector operation (P × Q) • R equals A) P × (Q • R). B) R • (P × Q). C) (P • R) × (Q • R). D) (P × R) • (Q × R ). 4. For finding the moment of the force F about the x-‐axis, the position vector in the triple scalar product should be ___ . A) rAC B) rBA C) rAB D) rBC 5. If r = {1 i + 2 j} m and F = {10 i + 20 j + 30 k} N, then the moment of F about the y-‐axis is ____ N·m. A) 10 B) -‐30 C) -‐40 D) None of the above. 6. In statics, a couple is defined as __________ separated by a perpendicular distance. A) two forces in the same direction B) two forces of equal magnitude C) two forces of equal magnitude acting in the same direction D) two forces of equal magnitude acting in opposite directions 7. The moment of a couple is called a _________ vector. A) Free B) Spin C) Romantic D) Sliding

8. The correct answer is: (B) 9. If three couples act on a body, the overall result is that A) The net force is not equal to 0. B) The net force and net moment are equal to 0. C) The net moment equals 0 but the net force is not necessarily equal to 0. D) The net force equals 0 but the net moment is not necessarily equal to 0 . 10. The correct answer is: (B) 11. You can determine the couple moment as M = r × F. If F = { -‐20 k} lb, then r is

A) rBC B) rAB

C) rCB D) rBA The correct answer is: (D)

12. The correct answer is: (C) 13. The line of action of the distributed load’s equivalent force passes through the ______ of the distributed load.

A) Centroid B) Mid-‐point C) Left edge D) Right edge 14. What is the location of FR, i.e., the distance d? A) 2 m B) 3 m C) 4 m D) 5 m E) 6 m 15. If F1 = 1 N, x1 = 1 m, F2 = 2 N and x2 = 2 m, what is the location of FR, i.e., the distance x. A) 1 m B) 1.33 m C) 1.5 m D) 1.67 m E) 2 m 16. FR = ____________ A) 12 N B) 100 N C) 600 N D) 1200 N 17. x = __________. A) 3 m B) 4 m

C) 6 m D) 8 m

18. The correct answer is: (B) 19. The moment of force F about point O is defined as MO = ___________ . A) r x F B) F x r C) r • F D) r * F 20. If M = r × F, then what will be the value of M • r ? A) 0 B) 1

C) r 2 F D) None of the above. 21. The correct answer is: (D) 22. If r = { 5 j } m and F = { 10 k } N, the moment r x F equals { _______ } N·m. A) 50 i B) 50 j C) –50 i D) – 50 j E) 0 23. Using the CCW direction as positive, the net moment of the two forces about point P is A) 10 N ·m B) 20 N ·m C) -‐ 20 N ·m D) 40 N ·m E) -‐ 40 N ·m

24. A general system of forces and couple moments acting on a rigid body can be reduced to a ___ . A) single force B) single moment C) single force and two moments D) single force and a single moment 25. The original force and couple system and an equivalent force-‐couple system have the same _____ effect on a body. A) internal B) external C) internal and external D) microscopic 26. Consider two couples acting on a body. The simplest possible equivalent system at any arbitrary point on the body will have A) One force and one couple moment. B) One force. C) One couple moment. D) Two couple moments. 27. The forces on the pole can be reduced to a single force and a single moment at point ____ . A) P B) Q C) R D) S E) Any of these points. 28. For this force system, the equivalent system at P is ___________ . A) FRP = 40 lb (along +x-‐dir.) and MRP = +60 ft ·lb B) FRP = 0 lb and MRP = +30 ft · lb C) FRP = 30 lb (along +y-‐dir.) and MRP = -‐30 ft ·lb D) FRP = 40 lb (along +x-‐dir.) and MRP = +30 ft ·lb 29. Consider three couples acting on a body. Equivalent systems will be _______ at different points on the body. A) Different when located B) The same even when located C) Zero when located D) None of the above.

R

ZS

Q

P

XY

Chapter 5: Statics

1. If a support prevents translation of a body, then the support exerts a ___________ on the body. A) Couple moment B) Force C) Both A and B. D) None of the above 2. Internal forces are _________ shown on the free body diagram of a whole body. A) Always B) Often C) Rarely D) Never 3. The beam and the cable (with a frictionless pulley at D) support an 80 kg load at C. In a FBD of only the beam, there are how many unknowns? A) 2 forces and 1 couple moment B) 3 forces and 1 couple moment C) 3 forces D) 4 forces 4. If the directions of the force and the couple moments are both reversed, what will happen to the beam? A) The beam will lift from A. B) The beam will lift at B. C) The beam will be restrained. D) The beam will break. 5. Internal forces are not shown on a free-‐body diagram because the internal forces are_____. (Choose the most appropriate answer.) A) Equal to zero B) Equal and opposite and they do not affect the calculations C) Negligibly small D) Not important 6. How many unknown support reactions are there in this problem? A) 2 forces and 2 couple moments B) 1 force and 2 couple moments C) 3 forces D) 3 forces and 1 couple moment

7. The three scalar equations ∑ FX = ∑ FY = ∑ MO = 0, are ____ equations of equilibrium in two dimensions.

A) Incorrect B) The only correct C) The most commonly used D) Not sufficient

8. A rigid body is subjected to forces as shown. This body can be considered as a ______ member. A) Single-‐force B) Two-‐force C) Three-‐force D) Six-‐force 9. For this beam, how many support reactions are there and is the problem statically determinate?

A) (2, Yes) B) (2, No) C) (3, Yes) D) (3, No)

10. The beam AB is loaded and supported as shown: a) how many support reactions are there on the beam, b) is this problem statically determinate, and c) is the structure stable?

A) (4, Yes, No) B) (4, No, Yes) C) (5, Yes, No) D) (5, No, Yes) 11. Which equation of equilibrium allows you to determine FB right away? A) ∑ FX = 0 B) ∑ FY = 0 C) ∑ MA = 0 D) Any one of the above. 12. A beam is supported by a pin joint and a roller. How many support reactions are there and is the structure stable for all types of loadings? A) (3, Yes) B) (3, No) C) (4, Yes) D) (4, No) 13. If a support prevents rotation of a body about an axis, then the support exerts a ________ on the body about that axis. A) Couple moment B) Force C) Both A and B. D) None of the above.

14. When doing a 3-‐D problem analysis, you have ________ scalar equations of equilibrium.

A) 3 B) 4 C) 5 D) 6 15. The rod AB is supported using two cables at B and a ball-‐and-‐socket joint at A. How many unknown support reactions exist in this problem?

A) 5 force and 1 moment reaction B) 5 force reactions C) 3 force and 3 moment reactions D) 4 force and 2 moment reactions 16. If an additional couple moment in the vertical direction is applied to rod AB at point C, then what will happen to the rod? A) The rod remains in equilibrium as the cables provide the necessary support reactions. B) The rod remains in equilibrium as the ball-‐and-‐socket joint will provide the necessary resistive reactions. C) The rod becomes unstable as the cables cannot support compressive forces. D) The rod becomes unstable since a moment about AB cannot be restricted. 17. A plate is supported by a ball-‐and-‐socket joint at A, a roller joint at B, and a cable at C. How many unknown support reactions are there in this problem? A) 4 forces and 2 moments B) 6 forces C) 5 forces D) 4 forces and 1 moment 18. What will be the easiest way to determine the force reaction BZ ? A) Scalar equation ∑ FZ = 0 B) Vector equation ∑ MA = 0 C) Scalar equation ∑ MZ = 0 D) Scalar equation ∑ MY = 0

Chapter 6: Statics 1. In the method of sections, generally a “cut” passes through no more than _____ members in which the forces are unknown. A) 1 B) 2 C) 3 D) 4 2. If a simple truss member carries a tensile force of T along its length, then the internal force in the member is ______ . A) Tensile with magnitude of T/2 B) Compressive with magnitude of T/2 C) Compressive with magnitude of T D) Tensile with magnitude of T 3. Can you determine the force in member ED by making the cut at section a-‐a? Explain your answer. A) No, there are 4 unknowns. B) Yes, using Σ MD = 0 . C) Yes, using Σ ME = 0 . D) Yes, using Σ MB = 0 . 4. If you know FED, how will you determine FEB ? A) By taking section b-‐b and using Σ ME = 0 B) By taking section b-‐b, and using Σ FX = 0 and Σ FY = 0 C) By taking section a-‐a and using Σ MB = 0 D) By taking section a-‐a and using Σ MD = 0 5. As shown, a cut is made through members GH, BG and BC to determine the forces in them. Which section will you choose for analysis and why? A) Right, fewer calculations. B) Left, fewer calculations. C) Either right or left, same amount of work. D) None of the above, too many unknowns. 6. When determining the force in member HG in the previous question, which one equation of equilibrium is best to use? A) Σ MH = 0 B) Σ MG = 0 C) Σ MB = 0 D) Σ MC = 0

7. Frames and machines are different as compared to trusses since they have ___________. A) Only two-‐force members B) Only multiforce members C) At least one multiforce member D) At least one two-‐force member 8. Forces common to any two contacting members act with ______ on the other member. A) Equal magnitudes but opposite sense B) Equal magnitudes and the same sense C) Different magnitudes but opposite sense D) Different magnitudes but the same sense 9. The figures show a frame and its FBDs. If an additional couple moment is applied at C, then how will you change the FBD of member BC at B?

A) No change, still just one force (FAB) at B. B) Will have two forces, BX and BY, at B. C) Will have two forces and a moment at B. D) Will add one moment at B. 10. The figures show a frame and its FBDs. If an additional force is applied at D, then how will you change the FBD of member BC at B? A) No change, still just one force (FAB) at B. B) Will have two forces, BX and BY, at B. C) Will have two forces and a moment at B. D) Will add one moment at B. 11. When determining the reactions at joints A, B, and C, what is the minimum number of unknowns for solving this problem? A) 3 B) 4 C) 5 D) 6 12. For the above problem, imagine that you have drawn a FBD of member AB. What will be the easiest way to write an equation involving unknowns at B? A) ∑ MC = 0 B) ∑ MB = 0 C) ∑ MA = 0 D) ∑ FX = 0

13. One of the assumptions used when analyzing a simple truss is that the members are joined together by __________. A) Welding B) Bolting C) Riveting D) Smooth pins E) Super glue 14. When using the method of joints, typically _________ equations of equilibrium are applied at every joint.

A) Two B) Three C) Four D) Six 15. Truss ABC is changed by decreasing its height from H to 0.9 H. Width W and load P are kept the same. Which one of the following statements is true for the revised truss as compared to the original truss? A) Force in all its members have decreased. B) Force in all its members have increased. C) Force in all its members have remained the same. D) None of the above. 16. For this truss, determine the number of zero-‐force members.

A) 0 B) 1 C) 2 D) 3 E) 4

17. Using this FBD, you find that FBC = – 500 N. Member BC must be in __________. A) Tension B) Compression C) Cannot be determined 18. For the same magnitude of force to be carried, truss members in compression are generally made _______ as compared to members in tension. A) Thicker B) Thinner C) The same size

Chapter 7: Internal Forces 1. In a multiforce member, the member is generally subjected to an internal _________.

A) Normal force B) Shear force C) Bending moment D) All of the above.

2. In mechanics, the force component V acting tangent to, or along the face of, the section is called the _________ .

A) Axial force B) Shear force C) Normal force D) Bending moment

3. A column is loaded with a vertical 100 N force. At which sections are the internal loads the same? A) P, Q, and R B) P and Q C) Q and R D) None of the above. 4. A column is loaded with a horizontal 100 N force. At which section are the internal loads largest? A) P B) Q

C) R D) S 5. Determine the magnitude of the internal loads (normal, shear, and bending moment) at point C.

A) (100 N, 80 N, 80 N m) B) (100 N, 80 N, 40 N m) C) (80 N, 100 N, 40 N m) D) (80 N, 100 N, 0 N m ) 6. A column is loaded with a horizontal 100 N force. At which section are the internal loads the lowest?

A) P B) Q C) R D) S

Chapter 8: Friction 1. A friction force always acts _____ to the contact surface.

A) Normal B) At 45° C) Parallel D) At the angle of static friction

2. If a block is stationary, then the friction force acting on it is ________ .

A) ≤ µs N B) = µs N C) ≥ µs N D) = µk N

3. A 100 lb box with a wide base is pulled by a force P and µs = 0.4. Which force orientation requires the least force to begin sliding?

A) P(A) B) P(B) C) P(C) D) Can not be determined 4. A ladder is positioned as shown. Please indicate the direction of the friction force on the ladder at B.

A) ↑ B) ↓ C) D) 5. A 10 lb block is in equilibrium. What is the magnitude of the friction force between this block and the surface? A) 0 lb B) 1 lb C) 2 lb D) 3 lb 6. The ladder AB is positioned as shown. What is the direction of the friction force on the ladder at B. A) B) C) ← D) ↑

Chapter 9: Centroid, Center of Gravity, and Center of Mass 1. The _________ is the point defining the geometric center of an object.

A) Center of gravity B) Center of mass C) Centroid D) None of the above

2. To study problems concerned with the motion of matter under the influence of forces, i.e., dynamics, it is necessary to locate a point called ________. A) Center of gravity B) Center of mass C) Centroid D) None of the above 3. The steel plate with known weight and non-‐uniform thickness and density is supported as shown. Of the three parameters (CG, CM, and centroid), which one is needed for determining the support reactions? Are all three parameters located at the same point?

A) (center of gravity, no) B) (center of gravity, yes) C) (centroid, yes) D) (centroid, no)

4. When determining the centroid of the area above, which type of differential area element requires the least computational work? A) Vertical B) Horizontal C) Polar D) Any one of the above. 5. If a vertical rectangular strip is chosen as the differential element, then all the variables, including the integral limit, should be in terms of _____ . A) x B) y C) z D) Any of the above. 6. If a vertical rectangular strip is chosen, then what are the values of x and y? A) (x , y) B) (x / 2 , y / 2) C) (x , 0) D) (x , y / 2)

7. A composite body in this section refers to a body made of ____. A) Carbon fibers and an epoxy matrix B) Steel and concrete C) A collection of “simple” shaped parts or holes D) A collection of “complex” shaped parts or holes

8. The composite method for determining the location of the center of gravity of a composite body requires _______.

A) Integration B) Differentiation C) Simple arithmetic D) All of the above.

9. Based on the typical centroid information, what is the minimum number of pieces you will have to consider for determining the centroid of the area shown at the right?

A) 1 B) 2 C) 3 D) 4 10. A storage box is tilted up to clean the rug underneath the box. It is tilted up by pulling the handle C, with edge A remaining on the ground. What is the maximum angle of tilt (measured between bottom AB and the ground) possible before the box tips over? A) 30° B) 45 ° C) 60 ° D) 90 ° 11. A rectangular area has semicircular and triangular cuts as shown. For determining the centroid, what is the minimum number of pieces that you can use? A) Two B) Three C) Four D) Five 12. For determining the centroid of the area, two square segments are considered; square ABCD and square DEFG. What are the coordinates (x, y ) of the centroid of square DEFG? A) (1, 1) m B) (1.25, 1.25) m C) (0.5, 0.5 ) m D) (1.5, 1.5) m

Chapter 10: Area Moment of Inertia 1. The definition of the Moment of Inertia for an area involves an integral of the form A) ∫ x dA. B) ∫ x2 dA. C) ∫ x2 dm. D) ∫ m dA. 2. Select the SI units for the Moment of Inertia for an area. A) m3 B) m4 C) kg·m2 D) kg·m3 3. A pipe is subjected to a bending moment as shown. Which property of the pipe will result in lower stress (assuming a constant cross-‐sectional area)? A) Smaller Ix B) Smaller Iy C) Larger Ix D) Larger Iy 4. In the figure to the right, what is the differential moment of inertia of the element with respect to the y-‐axis (dIy)? A) x2 y dx B) (1/12) x3 dy C) y2 x dy D) (1/3) y dy 5. When determining the MoI of the element in the figure, dIy equals A) x 2 dy B) x 2 dx C) (1/3) y 3 dx D) x 2.5 dx 6. Similarly, dIx equals

A) (1/3) x 1.5 dx B) y 2 dA C) (1 /12) x 3 dy D) (1/3) x 3 dx

7. The parallel-‐axis theorem for an area is applied between A) An axis passing through its centroid and any corresponding parallel axis. B) Any two parallel axis. C) Two horizontal axes only. D) Two vertical axes only. 8. The moment of inertia of a composite area equals the ____ of the MoI of all of its parts.

A) Vector sum B) Algebraic sum (addition or subtraction) C) Addition D) Product

9. For the area A, we know the centroid’s (C) location, area, distances between the four parallel axes, and the MoI about axis 1. We can determine the MoI about axis 2 by applying the parallel axis theorem ___ . A) Between axes 1 and 3 and then between the axes 3 and 2. B) Directly between the axes 1 and 2. C) Between axes 1 and 4 and then axes 4 and 2. D) None of the above. 10. For the same case, consider the MoI about each of the four axes. About which axis will the MoI be the smallest number? A) Axis 1 B) Axis 2 C) Axis 3 D) Axis 4 E) Can not tell. 11. For the given area, the moment of inertia about axis 1 is 200 cm4 . What is the MoI about axis 3 (the centroidal axis)? A) 90 cm 4 B) 110 cm 4 C) 60 cm 4 D) 40 cm 4 12. The moment of inertia of the rectangle about the x-‐axis equals A) 8 cm 4. B) 56 cm 4 . C) 24 cm 4 . D) 26 cm 4 .

Chapter 10 (cont.): Mass Moment of Inertia 1. The formula definition of the mass moment of inertia about an axis is ___________ . A) ∫ r dm B) ∫ r2 dm C) ∫ m dr D) ∫ m2 dr 2. The parallel-‐axis theorem can be applied to determine ________ . A) Only the MoI B) Only the MMI C) Both the MoI and MMI D) None of the above. Note: MoI is the moment of inertia of an area and MMI is the mass moment inertia of a body 3. Consider a particle of mass 1 kg located at point P, whose coordinates are given in meters. Determine the MMI of that particle about the z axis. A) 9 kg·m2 B) 16 kg·m2 C) 25 kg·m2 D) 36 kg·m2 4. Consider a rectangular frame made of four slender bars with four axes (zP, zQ, zR and zS) perpendicular to the screen and passing through the points P, Q, R, and S respectively. About which of the four axes will the MMI of the frame be the largest? A) zP B) zQ C) zR D) zS E) Not possible to determine 5. A particle of mass 2 kg is located 1 m down the y-‐axis. What are the MMI of the particle about the x, y, and z axes, respectively? A) (2, 0, 2) B) (0, 2, 2) C) (0, 2, 2) D) (2, 2, 0) 6. Consider a rectangular frame made of four slender bars and four axes (zP, zQ, zR and zS) perpendicular to the screen and passing through points P, Q, R, and S, respectively. About which of the four axes will the MMI of the frame be the lowest? A) zP B) zQ C) zR D) zS E) Not possible to determine.

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Mekanika Teknik