MEAM 535 Advanced Dynamics

Fall 1999

Homework #8

Material: painted aluminum; Outer diameter = 192 inches
1. The best way to master the techniques of computing the indertial properties of rigid bodies is to take a complex problem of a realistic structure. Consider the "split button" modern sculpture on Penn's campus in front of the Van Pelt library. The geometry information is given below. For the bigger part of the button, compute:
   • The center of mass (choose the center of the big circle as the origin; and fix a Cartesian frame there with x and y axes horizontal and z-axis vertical)
   • Moments of inertia about the center of mass (use the same Cartesian frame as above, but displaced to the center of mass)
   • The principal moments of inertia about the center of mass
   Density of aluminum = 0.1 lb/in^3
   Read simpler problems worked out in most dynamic books, including our texts, before you do this problem.
   
   

2. A thin homogeneous disk of mass m and radius a is held by a fork-ended horizontal shaft AB with an extension beyond B. The disk rotates about the z-axis and the shaft about the x-axis with angular velocities shown in the figure. Both the angular velocities are constant. Determine the dynamic reaction forces at bearings A and B.
   

3. An old airplane has a single four-bladed propeller which weighs 250 lb and has a radius of gyration of 32 inches. Knowing that the propeller rotates at 1800 rpm counter-clockwise as seen from the front, determine the magnitude of the couple exerted by the propeller on its shaft and resulting effect on the airplane when the pilot executes a horizontal turn of 1500-ft radius to the left at a speed of 375 mph.
   Note: radius of gyration is equal to the square root of the ratio of the moment of inertia to the mass.