MATHalinoEngineering Math ReviewProblem 818
A hollow square cross section consists of an 8 in. by 8 in. square from which is subtracted a concentrically placed square 4 in. by 4 in. Find the polar moment of inertia and the polar radius of gyration with respect to a z axis passing through one of the outside corners.
Problem 817
Determine the moment of inertia and radius of gyration with respect to a polar centroidal axis of the cross section of a hollow tube whose outside diameter is 6 in. and inside diameter is 4 in.
Problem 816
A rectangle is 3 in. by 6 in. Determine the polar moment of inertia and the radius of gyration with respect to a polar axis through one corner.
Moment of Inertia
Moment of inertia, also called the second moment of area, is the product of area and the square of its moment arm about a reference axis.
Moment of inertia about the x-axis:
Problem 726
Locate the centroid of the shaded area enclosed by the curve y2 = ax and the straight line shown in Fig. P-726. Hint: Observe that the curve y2 = ax relative to the y-axis is of the form y = kx2 with respect to the x-axis.
Problem 725
Repeat Problem 239 without using integration.
Problem 724
Find the coordinates of the centroid of the shaded area shown in Fig. P-724.
Problem 723
Locate the centroid of the shaded area in Fig. P-723.
Problem 722
Locate the centroid of the shaded area in Fig. P-722 created by cutting a semicircle of diameter r from a quarter circle of radius r.
Problem 721
Refer again to Fig. P-714. To what value should the 6-in. width of
the flange be changed so that the centroid of the area is 2.5 in. above the base?
