the moments of inertia Ix, Iy, I0 for a lamina in the shape of an isosceles right triangle with equal sides of length a if the density at any point is proportional to the square of the distance from the vertex opposite the hypotenuse. (Assume that the coefficient of proportionality is k, and that the lamina lies in the region bounded by x = 0, y = 0, and y = a − x). Ix = Iy = I0 =

the moments of inertia Ix, Iy, I0 for a lamina in the shape of an isosceles right triangle with equal sides of length a if the density at any point is proportional to the square of the distance from the vertex opposite the hypotenuse. (Assume that the coefficient of proportionality is k, and that the lamina lies in the region bounded by x = 0, y = 0, and y = a − x). Ix = Iy = I0 =

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter9: Moments And Products Of Inertia Of Areas

Section: Chapter Questions

Problem 9.87RP

See similar textbooks

Similar questions

Using integration, compute the polar moment of inertia about point O for the circular sector. Check your result with Table 9.2.
Compute the principal centroidal moments of inertia for the plane area.
For the section below: а. Determine the moment of inertia with respect to the X-axis. b. Determine the moment of inertia with respect to the Y-axis. C. Determine the moment of inertia with respect to the X'-axis. 40 mm 80 80 30° tw = 40 mm 40 mm 200 mm 9. 300 mm 220 mm
Find the moment of inertia about the x-axis of a thin plate bounded by the parabola x = 7y - 3y² and the line x + 2y = 0 if 8(x,y) = x + 2y. Choose the correct sketch of the plate described above. O A. Q O A. SS F(x,y) dy dx O B. OB. F(x,y) dx dy Q Select the order of integration that will make the computations easier and fill in the limits of integration in your choice. G O C. O D. Use the given density function 8 to write the appropriate integrand F(x,y) for finding the moment of inertia. Then substitute into the correct integral from the previous step and evaluate to find the moment of inertia for the plate. The moment of inertia is (Simplify your answer.) Q Q ✔
Determine the moment reaction at the fixed support A. The forces P = 218 N, F =436 N, and Q = 218 N are parallel to the y, x and z axis respectively. The moment MCB = 436 N.m is around the line CB. P B 2 m 1 m 2.5 m McB 2 m D F O A. MA = -872.0k N.m O B. MA = 218i + -654.0j + -327.0k N.m O C. MA = -436.0j N.m O D. MA = -654.0j + -545.0k N.m O E. MA = 545.0i + -545.0j + -545.0k N.m
Determine the following statement that is true regarding Mohr's Circle. Reference points on Mohr's Circle from two perpendicular axes on the cross-section can lie at angles smaller than 180 degrees relative to each other. Mohr's Circle can't be used to identify angles between principal and non-principal axes. Mohr's Circle contains all possible moment of inertia and product of inertia values for a given fixed area about all rotated axes around the same origin. A reference point on Mohr's Circle that corresponds to one of the principal axes can lie at coordinates of (492, 18.7). The center of Mohr's Circle can only be calculated using principal moments of inertia.
Which of the following equations define the moment of inertia about the x-axis of the area shown in the Figure below? HINT: I. = (bh³)/36 h 3
Determine the moment of inertia (in mm4) of the given figure with respect to x axis. Assume y=98 mm and z=49 mm. Round off only on the final answer expressed in whole number.
For the orange shaded area shown in the image below, if the coefficients for the function a = 1.4 and b= 2.9, determine its area moment of inertia ly about the given y- axis. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point. а - х y2 : %3D Your Answer:
Determine the principle moments of inertia and the orientation of the principle axes for the section shown below. Units are in millimeters and centroid of the section is given. Use the given partition for areas. Hint: I = I, due to the symmetry. Draw the Mohr's circle for the moments of inertia show principle axes. to- C(ag); centroid 20 X =j = 8,33 20 I, + 1, (1, -ly (1, – 1,)/2 tan 20, + Iy
Determine the area moments of inertialx and ly. Given that c = 0.94 in. lx || 4 in. || y -0.5 in. The area moments of inertia /x and ly are as follows: 4 in. 0.5 in. 4 in. 4 in. X
Calculate the Moment of Inertia of the given lamina, for the dimensions B=20mm, D=30mm, b=15mm and d=25mm. y A B E C.G X - X d D H D b B