17-6. The sphere is formed by revolving the shaded area around the x axis. Determine the moment of inertia I, and express the result in terms of the total mass m of the sphere. The material has a constant density p. * + y? = r?
Q: R6-5. Determine the moment of inertia for the area about the x axis. y= 2 m 4 m
A: Take a horizontal thin plate of thickness dy parallel to x-axis Area of thin plate
Q: 17-2. The solid cylinder has an outer radius R, height h, and is made from a material having a…
A: Consider a cylindrical element of mass dm and radius dr The mass of the cylindrical element will be…
Q: 10-42. Determine the moment of inertia of the beam's cross- sectional area about the x axis. 30 mm
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Q: *17-8. The hemisphere is formed by rotating the shaded area around the y axis. Determine the moment…
A: Given A Hemisphere Total mass = m Density = ρ To find Determine the moment of inertia Iy
Q: 18-31. Determine the moment of inertia for the beam's cross-sectional area about the yaxis. 3 in D 1…
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Q: 6-62. Determine the product of inertia of the shaded area of Fig. P6-62. The equation of the curve…
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Q: F6-19. Determine the moment of inertia of the cross- sectional area of the channel with respect to…
A: The sectional representation of the given problem is: Determine the centroid of the section: X…
Q: 17-23. Determine the moment of inertia of the overhung crank about the x' axis. The material is…
A: Step 1: The density of steel is ρ = 7.85 Mg/m3 = 7.85 x 103 kg/m3 The length between the xx’ is…
Q: *17-16. Determine the mass moment of inertia of the thin plate about an axis perpendicular to the…
A: Given Data: The radius of the circular plate is r = 200 mm. The side of the square hole in the…
Q: 21-10. Determine the radii of gyration k, and k, for the solid formed by revolving the shaded area…
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Q: 10-99. Determine the mass moment of inertia of the thin plate about an axis perpendicular to the…
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Q: 21-15. Determine the moment of inertia of both the 1.5-kg rod and 4-kg disk about the z' axis. 300…
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Q: *17-4. The paraboloid is formed by revolving the shaded area around the x axis. Determine the radius…
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Q: 17-19. Determine the moment of inertia of the wheel about an axis which is perpendicular to the page…
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Q: This is a dynamics problem. Answer: IO = 1.13 kg*m2
A: The given geometry consists of a plate from which a square shape hole has been cut. Thus, there are…
Q: 21-7. Determine the product of inertia I, of the object formed by revolving the shaded area about…
A: Given curve equation, y2 = 3x x’ = 5 ft Writing the equation for the elementary mass in case this…
Q: 17-1. Determine the moment of inertia 1, for the slender rod. The rod's density p and…
A: Given Mass of the rod = m Length of the rod = l Cross-sectional area = A Rod density = ρ To find…
Q: This is a dynamics problem. Answer: kx = 1.2 in
A: The radius of gyration is the square root of the ratio of moment of inertia and mass. Thus, for…
Q: F6-15. Determine the moment of inertia of the area about the y axis. y' 1m 1m
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Q: 10-33. Determine the moment of inertia I of the shaded axis. area about the y 100 mm --100 mm 150 mm…
A: Dividing the diagram into three parts Part 1 :- A rectangle OABC, Part 2:- A triangle BCD and Part…
Q: 6-57. Determine the moment of inertia for the area about the y axis. -y² = 1 - 0.5x 1m
A: Given Data: The given curve is y2= 1-0.5x. The curve extends from (0,1) to (2,0). To determine the…
Q: *21-20. Determine the moment of inertia of the disk about the axis of shaft AB. The disk has a mass…
A: Given data, Mass of the disk, m=15 kg Radius of the shaft, R=150 mm
Q: 21-11. Determine the moment of inertia of the cylinder with respect to the a-a axis of the cylinder.…
A: Given Data: The mass of the cylinder is m. Radius of cylinder is a. Height of cylinder is h. The…
Q: F10-2. Determine the moment of inertia of the shade area about thex axis 1m -1r
A: Consider a strip of thickness dy as shown above.
Q: R6-6. Determine the area moment of inertia of the area about the y axis. 4y=4 - 1m 2m
A: Given Data: The equation of the curve is 4y = 4-x2. The curve extends from (-2,0) to (2,0). The…
Q: 17-7. The frustum is formed by rotating the shaded area around the x axis. Determine the moment of…
A: Given : The density of the frustum material is ρ. The total mass of the frustum is m. The major…
Q: *21-4. Determine the moments of inertia I, and I, of the paraboloid of revolution. The mass of the…
A: Given Mass of paraboloid = 20 slug To find Moment of inertia About x axis About y axis
Q: *21-16. The bent rod has a mass of 3 kg/m. Determine the moment of inertia of the rod about the 0-a…
A: Given data The mass of rod, m = 3 kg/m. The bent rod is subdivided into three segments and the…
Q: 6-66. Determine the moment of inertia about the y axis 7 + 4y² = 4 1m
A: Draw the schematic diagram for the above system.
Q: 10-57. Determine the product of inertia of the shaded area with respect to the x and y axes. b b
A:
Q: F6-17. Determine the moment of inertia of the cross- sectional area of the beam about the centroidal…
A: The front view of the given cross section can be drawn as, The given cross-sectional area is made…
Q: *10-40. Locate the centroid ỹ of the composite area, then determine the moment of intertia of this…
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Q: 10-6. Determine the moment of inertia for the shaded area about the y axis.
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Q: *10-8. Determine the moment of inertia of the area about the y axis. – y² = 1 – 0.5x 1 m 1 m -2 m -
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Q: 21-5. Determine by direct integration the product of inertia I,; for the homogeneous prism. The…
A: To determine: Product of inertia Iyz for the homogenous prism Let the mass of the differential…
Q: F6-18. Determine the moment of inertia of the cross- sectional area of the beam about the centroidal…
A: Dimensions are height = 200 mm thickness = 30 mm
Q: 21-3. Determine moment of inertia !, of the solid formed by revolving the shaded area around the x…
A: ρ = 12 slug/ ft3 Taking a small section as shown in figure,
Q: 21-19. Determine the moment of inertia of the composite body about the aa axis. The cylinder weighs…
A: Given data: d=2 fth=2 ftmcylinder=20 lbmhemi-sphere=10 lb
Q: This is a dynamics problem. Answers: m = pi*h*R2 [k + (aR2)/2] , Iz = [(pi*h*R4)/2] * [k +…
A: Let us consider an elemental shell at a radius r of thickness dr as shown below –
Q: 10-7. Determine the moment of inertia for the shaded area about the x axis. y 1-0.5x 1m 2 m Probs.…
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Q: F6-16. Determine the moment of inertia of the area about the y axis. Im -1m-
A: Consider an elemental strip of width dx in the shaded region. The height of the strip is equal to…
Q: 10-55. Determine the product of inertia of the shaded area with respect to the x and y axes. y h
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Q: 21-17. The bent rod has a weight of 1.5 lb/ft. Locate the center of gravity G(I, ỹ) and determine…
A: The weight density is given as γ = 1.5 lb/ft a= 1 ft and b= ft On substitution, we get x' = 0.667…
Q: 10-10. Determine the moment of inertia of the area about the x axis. Solve the problem in two ways,…
A:
Q: 9-42. Determine the mass moment of inertia and the radius of gyration about the centroidal wis…
A: Given Mass, m = 64.4 lb Diameter, d = 2 ft Radius, r = 1 ft Fine Mass moment of…
Q: *21-12. Determine the moment of inertia I of the composite plate assembly. The plates have a…
A: Draw the schematic diagram of the assembly.
Q: 21-2. Determine the moment of inertia of the cone with respect to a vertical ỹ axis passing through…
A: Consider the diagram shown below for the elemental mass.
Q: 6-62. Determine the product of inertia of the shaded area of Fig. P6-62. The equation of the curve…
A: Consider a small element dx at x distance from the origin as shown below :
Q: 17-5. Determine the radius of gyration k, of the body. The specific weight of the material is y =…
A: Given data: The specific weight of the material is γ=380 lbft3 A small element on the body is as…
Q: *17-16. The two steel channels are to be laced together to form a 9-m-long bridge column assumed to…
A: Moment of inertia of the whole section about the x axis is Iwx=2Ix=221.60×106=43.20×106 mm4 Moment…
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- Determine the moment of inertia of the thin plate about an axis perpendicular to the page and passing through the pin at O. The plate has a hole in its center. Its thickness is 50 mm and the material has a density of 50 kg/m^3The pendulum consists of a 8-kg circular plate and a 3-kg slender rod. Determine the radius of gyration of the pendulum about an axis perpendicular to the page and passing through point O. kO = ?he assembly consists of a disk having a mass of 5 kg and slender rods ABand DC which have a mass of 2 kg/m. If L = 0.6 m, determine the moment of inertia and radius of gyration of the assembly about an axis perpendicular to the page and passing through point O. Also, find the position of the center of mass Gin relation to O. Please explain steps
- The pendulum consists of two rods AB and OC, which have a mass density of 3kg/m. The thin disk has a mass of 12 kg/m2. Determine the location of the center of mass of the pendulum, calculate the mass moment of inertia about the axis perpendicular to the sheet and passing through point O. Report only the moment of inertia in terms of [kg m2].H6. Find the position of the cross-section’s centroid. Then, determine the moments of inertia of horizontal & vertical axes through the centroid. (I'm not sure if the width of the verticle rectangle is needed or not. If it is, assume 5 mm.)A) Determine the position of the center of gravity of the figure's structure. B)Determine the moment of inertia of mass with respect to the x' axis that passes through the structure's center of gravity and is parallel to the x axis. The cone has a density of 600 kg/m3 and the cylinder a density of 800 kg/m3. Consider H = 83
- The pendulum consists of two rods AB and OC, which have a mass density of 3kg/m. The thin disk has a mass of 12 kg/m2. Determine the location of the center of mass of the pendulum, calculate the mass moment of inertia about the axis perpendicular to the sheet and passing through point G. Report only the moment of inertia in terms of [kg m2].Determine the moment of inertia of mass with respect to the x' axis that passes through the structure's center of gravity and is parallel to the x axis. The cone has a density of 6000 kg/m3 and the cylinder a density of 8000 kg/m3. Consider H = 83The paraboloid is formed by revolving the shaded area around the x axis. The material has a constant density ρ. Determine the moment of inertia about the x axis and express the result in terms of the total mass m of the paraboloid.
- Determine the mass of the R-134a.Locate the center of mass x̄ of the straight rod if itsmass per unit length is given by m = m0(1 + x2/L2).The pendulum consists of a 6.5- kg circular plate and a 2.5- kg slender rod. Determine the radius of gyration of the pendulum about an axis perpendicular to the page and passing through point O.