Expert Answer o Step1 a) For the given shaded area r = 12 cm L4 = 15 cm y.
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- For the purple region bounded by a parabola with vertex at (-1, 5) and the green line, solve y = -a(x – h)? + k for: a. Area b. Centroid c. Volume when revolved 230° about the green line (-2.1, 2.2) d. MOI and radius of gyration about the x-axis using horizontal strips. e. MOI and radius of gyration about the y-axis using vertical strips. f. MOI and radius of gyration about the z-axis (1, n)3:59O l 37.6 26) K/s REC Question v? = 400x Determine the moment of inertia for the shaded area shown about the x - (100 – x)- dy axis. 200 mm 100 mm 27:082021 BME 1205 Moment of Inertia Natukunda Faith's screen50 mm 150 mm 150 mm 300 mm find the moment of inertia for this exercise, with the following formulas: Polar Jo= Iox + + Toy Iox - Icx + Adg² Toy = Icg + dobe ² Caculation of centroid attached below. use it to solve the question in red box asap Som Av 3com for Portion A₁ - the figure is symme about y-aris. 2=0. AL 120mm AALD Area of A₁ = 300x50 = 15000 Y₁ = y₁ y = 300 for Pation A2 Area Az = 50x300 = 15000 By Considering Centroid, from the Bottom of the section. 300+ 50 = ₁ + 3/2 = 325 Centroid (ā, y) = = [0₁ SE = 50mm A, Ya+ A₂4 0, A₁+A₂ 15000x150 +15000x325 15000 15000 (0.237.5)
- 16 - Find the center of gravity M (x,y,z) of the three-dimensional homogeneous ABCD wire in the figure by using the coordinate set. The dimensions of the wire are a= 24 cm, b= 36 cm. In which of the following options are the coordinates of the homogeneous wire in the x, y and z axes given correctly?A) (23.57 ; 11.43 ; 17.14)B) (23.57 ; 17.14 ; 11.43)C) (28.29 ; 13.71 ; 20.57)D) (20.61 ; 13.03 ; 9.08)E) (28.29 ; 20.57 ; 13.71)4. Find the Area Moment of Inertia Ix about the X-axis, if a = 7 inches, b = 14 inches h = 7 inches, and Y bar = 3.11 inches to the Centroid of the diagam from the base of the diagram. The X-axis is Ithe horizontal axis that goes through the Centroid (C) and is located 3.11 inches (Y bar) from the base of the diagram. %3D MacBook Air4 cm -10 cm Calculate the moment of inertia l, in the coordinate set (x,y) placed at the center of gravity of the section given 4 cm 10 om M in the figure. Write the result by rounding to the nearest whole number and specifying the unit. y5.5 cm
- Consider the triangle shown, and; a) Determine the location of centroid C(x,y) b) Moments of inertia components w.r.t x and y axes (Ix, Iy, Ixy) c) Principle moments of inertia (Imax, Imin) using Mohr's circle E 3 cm -3 cm 3 cm 3 cmIn civil construction it is very common to use L sections, angle, for comer pillars. Calculate the center of gravity L drawn below, informing the x coordinates with respect to the y axes and the Moment of Inertia Ix and Iy with respect to this center of gravity. Consider as measurements in centimeters, where: = 60 b= 90 Note: use Steiner's theorem 50 a 20QUESTION 1) In the section in which geometric properties are given in figure; Calculate the moments of inertia Ix, Iy, Ixy On the coordinate set placed at the center of the section (n= 3). 4em 4cm 4cm G 4cm 4cm 12cm 8cm 4cm 8em 4cm 8cm ++
- 1. Locate the centroid of the following figures. 90 mm : y a) b) 90 ty 4 in mm 3 in 120 X + 2 in 2 in 2 in A = A1 - A2 Ax = A1 x1 - A2 x2 А у%3DA1 y1 - A2 у2 A = A1 - A2 Ax = A1 x1 - A2 x2 А у 3DA1 y1 - А2 у2 2. Compute for the moment of inertia about xo and yo of the following figures. а) b) y 100 mm 100 mm 75 mm y 25 mm 120 mm 75 mm 50 mm 180 mm | = |1 - 12 |= 1 + 1219:49 wamap.org Compute the coordinates of the centroid (x, y) of the area shown. Also compute the area moment of intertia about the x' and y' axes with origin at the centroid. ул C 2013 Michael Swanbom cc 130 f a Variable Value 38 cm 18 cm 74 cm a Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. a b C The x coordinate of the centroid is x cm. The y coordinate of the centroid is y The moment of inertia about the x' axis going through the centroid is I' cm4. cm. The moment of inertia about the y' axis going through the centroid is I' cm4.The moment of inertia of a triangle of base 'b' and height 'h' about Y - Y axis passing through its center of gravity is Select one: dh³/36 bh/36 bh³/12 dh³/12 Shear forces and friction forces always acts along the surfaces and are an example of indirect forces. Select one: True False