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1. Consider the motion of an axially symmetric body in the absence of torques. Find the analytical solution for the Euler angles as a function of time.
2. Show that the ellipsoid of inertia of a cube of uniform density having an edge of length a, is a sphere for a set of axes whose origin is at the cube's center. What is the magnitude of the radius?
3. A thin uniform circular disk of mass M and radius rD, is mounted on a shaft which is pivoted clockwise at O about the vertical axis z. The shaft is perpendicular to the face of the disk and it defines the x2-axis; the mass of the shaft can be ignored. If the disk rolls without slipping and makes one complete revolution in a circle of radius R in a time 2-, write the expression for the angular momentum of the disk with respect to the axes x2 and x3 through 0.
4. A football is thrown such that on release its axis of symmetry is 10o above the horizon and its angular velocity is 2.5 rev/sec at an angle of 15° above the axis of symmetry. The moment of inertia of the football about the axis of symmetry is 4/9 times the moment of inertia about a perpendicular axis through its center of mass. Assuming torque free motion determine: a) The angle between the symmetry axis of the football and the axis of precession. b) The rate of precession of the football's symmetry axis c) The rate of the football's spin.
A slender rod 0.6 m long rotates about an axis perpendicular to its length and 0.14 m from its center of gravity. If the rod has a mass of 8 kg, determine its mass moment of inertia about this axis
Describe the differences among the three PLC types : rack/slot address based, tag based, and soft PLCDescribe the differences among the three PLC types : rack/slot address based, tag based, and soft PLC.
an airplane heads west at a 400 km per hour in a 50-km-per-hour northwest wind. find a vector that models the resulting
Draw a suitable schematic diagram for an isolation amplifier, and explain the operation of this device.
Calculate the change in frequency, velocity amplitude, and acceleration amplitude if the maximum deflection remains 10 cm.
1. Zinc selenide has a band gap of 2.58 eV. Over what range of wavelengths of visible light is it transparent? 2. Briefly explain why the magnitude of the ab- sorption coefficient (b in Equation 21.18) depends on the radiation wavelength.
plot schematics of stress vs strain and stress vs. strain rate for i creep deformation ii superplastic deformation and
a tensile member of 2024-0 aluminum alloy used for aircraft fuselage had an original cross-sectional area of 4.0square
an air standard otto cycle has a compression ratio of 9.5. at the beginning of the isentropic compression the working
An oven door consists of a layer of asbestos sandwiched between a layer of steel on the inner surface and a layer of wood on the outer face
8 kg of saturated water vapor is contained in a piston cylinder assembly at 15 bar. It is slowly cooled at constant pressure until it becomes all saturated liquid water. A) Determine how much heat was removed during the process B) what is the total w..
Find the horizontal and vertical area moment of inertias of the cross-section shown with respect to its centroid.
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