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Question 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.
Question 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?
Question 3 A thin uniform circular disk of mass M and radius r, is mounted on a shaft which is pivoted clockwise at 0 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 τ, write the expression for the angular momentum of the disk with respect to the axes x2 and x3 through 0.
Question 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 dehumidifier brings in saturated wet air (100 percent relative humidity) at 30°C and 1 atm, through an inlet of 8-cm diameter and average velocity 3 m/s. After some of the water vapor condenses and is drained off at the bottom, the somewhat drie..
What is the temperature 7 cm from the base if the rod is made of a) pure zinc b) lead c) pure gold. Which will be the hottest at this point?
A simplified model of a petroleum pump is shown in Fig. 1.99, where the rotary motion of the crank is converted to the reciprocating motion of the piston. Find the equivalent mass, meq of the system at location A.
When materials are joined, we create interfaces between the various components.
1 for an astm grain size of 8 approximately how many grains would there be per square centimeter a at a magnification
for the spring-mass-pulley system of figure 5-37 the moment of inertia of the pulley about the axis of rotation is j
Outside cool air at 15C and 40% relative humidity is mixed with inside air taken near the celling in a room at 32C and 70% relative humidity. Determine the relative humidity and temperature of the resultant air stream if the outside flow rate is 40 m..
Effective Matching of Surface Roughness, Concerning the effective matching of surface roughness using a lathe, I have been asked to quantify Ra = C1* s^C2 v^C3 Re^C4
Determine an equation that can be used to predict annual sales of these dolls. Make sure that all variables in your equation are significant at the 10% level.
a particle of mass m kg carrying q coulombs enters the space between two charged plates with the horizontal velocity
the central cubical area of an office building at sea level has a floor area of 4000 ft2 and is occupied by 30 people
A Rankine cycle power plant is being developed to operate an irrigation system. In this power plant solar energy will be used to boil a low boiling point fluid within glazed flat plate solar collectors. The working fluid that has been selected is the..
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