0.980 in. 0.25 in. 10.487 in. х 2 in. L3 x 2 x- 4 0.25 in. 3 in.

Q: Determine by direct integration the moment of inertia of the shaded area with respect to the x…

A: Given figure    Given mathermatical expression to calculate moment of inertia is

Q: Shown is the cross section of an idler roller. Determine its mass moment of inertia and its radius…

A: Write the expression of the mass of the bronze part. Write the expression of the mass of the…

Q: Two 20-mm steel plates are welded to a rolled S section as shown.Determine the moments of inertia…

A: Write the values of the S-section. Write the expression of the total area.

Q: 9.122 Determine by direct integration the mass moment of inertia with respect to the x axis of the…

A:

Q: Determine the moment of inertia and radius of gyration of the shaded area shown with respect to the…

A: Consider a horizontal elemental strip as shown below:

Q: 11B) The area moment of inertia about centroidal axis is the area moment of inertia about a parallel…

A: option C is the correct answer  i.e. less than

Q: A thin plate with a mass m was cut in the shape of a parallelogram as shown. Determine the mass…

A: We will consider the parallelogram as a square to make our calculation easier. Let's consider this…

Q: For the area indicated, determine the orientation of the principal axes at the origin and the…

A: Draw the diagram of the section.

Q: 31 Determine the percent reductions in both area and area moment of inertia about the y-axis caused…

A:

Q: To form a reinforced box section, two rolled W sections and two plates are welded together.…

A:

Q: Determine by direct integration the product of inertia of the given area with respect to the x and y…

A: Let us take a strip of thickness dx at a distance x as shown below, The area of the strip will be,…

Q: The machine element shown is fabricated from steel. The density of steel is 7850 kg/m³. Determine…

A: Given, a=35 mm,b=60 mm,c=20 mm,d=40 mm,e=70 mm,Density of steel, ρ=7850 kg/m2

Q: For the figure shown knowing that a = 1.00 cm and b = 4.00 cm, determine: (a) The centroid of the…

A:

Q: A thin plate with a mass m has the trapezoidal shape shown. Determine the mass moment of inertia of…

A: Given data To determine the mass moment of inertia of the plate with respect to

Q: Determine the percent reduction n in the polar moment of inertia of the square plate due to the…

A: It is required to determine reduction in polar moment of inertia about x axis due to circular hole

Q: Shown is the cross section of a molded flat-belt pulley. Determine its mass moment of inertia and…

A:

Q: A thin steel wire is bent into the shape shown. Denoting the mass per unit length of the wire by m’,…

A:

Q: Determine the moments of inertia and the product of inertia of the area of Prob. 9.72 with respect…

A: The given figure can be broken into two figures as shown below, Because of the symmetry of the…

Q: Determine the moments of inertia and the product of inertia of the area of Prob. 9.75 with respect…

A: Consider the diagram shown below for the given figure, Now the product of inertia about the…

Q: A piece of thin, uniform sheet metal is cut to form the machine component shown. Denoting the mass…

A: Given Data: The mass of the component is m. The area of the component can be determined as, Where…

Q: 90 10 10 10 20 Fig. 14b 30 10. 20 110 All dimensions are in 'mm'

A:

Q: For the area indicated, determine the orientation of the principal axes at the origin and the…

A: Given data Determine the product of inertia of the area shown with respect to the centroidal x and…

Q: Determine the polar moment of inertia and the polar radius of gyration of the rectangle shown with…

A: Given data To determine the polar moment of inertia and the polar radius of gyration of the…

Q: Determine the moments of inertia and the product of inertia of the area of Prob. 9.73 with respect…

A: First, we convert the given diagram into two parts as shown below : here the first and two parts…

Q: (a) Determine by direct integration the polar moment of inertia of the annular area shown. (b) Using…

A: Given Data: The outer radius of the annular area is R2. The inner radius of the annular area is R1.…

Q: For the L5 x 3 x 1/2-in. angle cross section shown, use Mohr’s circle to determine (a) the moments…

A: Dimension of L ,5 in X 3 in X 0.5 in

Q: By direct integration, determine the moments of inertia of the triangular area about the x- and…

A: For the triangular area, b = 7 in h = 15 in It is required to determine the moment of inertia of the…

Q: Using Mohr’s circle, determine for the quarter ellipse of Prob. 9.75 the moments of inertia and the…

A: I of rectangle=bd312Ixx=(100X8312)+2(8X32312+(8X32)(202)) mm4Ixx=252757.333…

Q: A custom-fabricated component for a machine consists of a steel (y = 0.28 lbf/in?), 5-in diameter…

A: The mass of the solid steel cylinder without any hole pattern is The mass of the bronze part is…

Q: A/35 Determine the percent reductions in both area and area moment of inertia about the y-axis…

A: Let the initial area be, A1=bh Now the reduced area is, ΔA=2b3·h-2h8=2b3·h-h4=bh2

Q: The machine element shown is fabricated from steel. Determine the mass moment of inertia of the…

A:

Q: Determine the moments of inertia and the product of inertia of the L127 x 76 x 12.7-mm angle cross…

A: Determine moment of inertia about different axis The mohr circle is defined by diameter XY

Q: A section of sheet steel 0.03 in. thick is cut and bent into the sheet metal machine component…

A: The figure is given as Mass of part 1 m1=γsgV1=γsgA1t=49032.21210.3750.0025=0.007133 lb.s2/ft Mass…

Q: Determine by direct integration the moment of inertia of the shaded area with respect to the y axis.

A: Given Data: The given curve is y=kx12. The curve extends from (0,0) to (a,b). The value of k can…

Q: the ratio moment of inertia of a rectangular shape to triangular shape having the same base width(b)…

A: The moment of Inertia of a plane area with respect to x and y axis respectively is defined by the…

Q: A thin plate with a mass m is cut in the shape of an equilateral triangle of side a . Determine the…

A: Each side of the given equilateral triangle is a units.             →Mass of the…

Q: By the method of this article, determine the moments of inertia about the x- and y-axes of the…

A: Find the moment of inertia about x and y axis.

Q: First Cluss Sample Problem 7/9: Determine the moments of inertia about the x- and y-axes for the…

A: Given Shaded area To find Moment about X and Y axis

Q: ),7-L X' |3.L 0,3-L

A:

Q: Determine for the quarter ellipse of Prob. 9.67 the moments of inertia and the product of inertia…

A:

Q: 9.21 Determine the polar moment of inertia and the polar radius of gyration of the rectangle shown…

A:

Q: The moments and product of inertia of an L4 x 3 x 1/4-in. angle cross section with respect to two…

A: I¯avg=12(I¯x+I¯y)=12(1.33+2.75)=2.040 in4I¯min=I¯avg-RR=2.040-0.692=1.348 in4

Q: Using Mohr’s circle, determine for the quarter ellipse of Prob. 9.67 the moments of inertia and the…

A: The expression to calculate the inertia along x-axis is, Ix=π162aa3=π2a4 The expression to calculate…

Q: Two L76 × 76 × 6.4-mm angles are welded to a C250 × 22.8 channel. Determine the moments of inertia…

A: Angle : A=929 mm2Ix=Iy=0.512×106 mm4 Channel: A=2890 mm2Ix=0.945×106 mm4Iy=28×106 mm4

Q: Two 20-mm steel plates are welded to a rolled S section as shown. Determine the moments of inertia…

A: Given, S section = S310 X 47.3

Q: Determine by direct integration the moment of inertia of the shaded area with respect to the y…

A: Draw the diagram considering a small element at a distance of x from the y-axis.

Q: A square hole is centered in and extends through the aluminum machine component shown. Determine (a)…

A: Given data: Figure with relevant details as shown   To determine: Value of 'a' for which MOI is…

Q: The moment of inertia with respect to the x and y axis have been computed and are known to be L =…

A:

Q: For the area indicated, determine the orientation of the principal axes at the origin and the…

A: Lets first assume two rectangle 1 and 2 Now we need to calculate x and y for both the…

Moment of Inertia

Inertia can be termed as a resistance offered by a body to change its state. A rigid body initially at rest will apply resistance when acted by an external force that tends to change its state of rest or velocity, or a body initially at motion will provide resistance in changing its state of velocity or motion for coming to a state of rest. In other words, Newton's first law of motion describes the law of inertia of a rigid body.