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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.
What is the probability that the strength is less than or equal to 5,000 psi. What is the probability that the strength is greater than 2,500 psi
the simple steam power cycle in prob 4.23 in modified in the following way. steam entering the turbine is expanded to
Impact of a Particle in a Circle A particle m is fired with initial velocity v0 from the intersection of a circle with radius R and the x-axis. Assume e = 1 and determine the coordinates of the third impact point of the particle with a wall in Fig..
A 50-hp, 230-V shunt motor has a field resistance of 17.7 Q and operates at full load when the line current is 181 A at 1,350 r/min. To increase the speed of the motor to 1,600 r/min, a resistance of 5.3 Q is "cut in" via the field rheostat; the l..
A 100 MW steam station uses coal of calorific value 6400 kcal/kg.- Calculate the coal consumption per hour when the station is delivering its full rated output.
a major automotive company is considering an agreement with a small manufacturer whereby it would be required to make
the inlet to a boiler of a carnot power cycle is at 5 mpa saturated liquid and the exit is saturated vapor. the
10 kg of gaseous oxygen is compressed in a piston-cylinder device from an initial state of .8 m3kg to a final state of
Knowing that the thin cylindrical shell shown is of mass m, thickness t, and height h, determine the mass moment of inertia of the shell with respect to the x axis
The uniform bar with end rollers weighs 60 lb and is supported by the horizontal and vertical surfaces and by the wire AC. Calculate the tension T in the wire and the reactions against the rollers at A and at B.
a small 4 oz particle is prokected with a horizontal velocity of 6ftsec into the top of smooth circular guide fixed in
The turbine develops 250 KW of power, which is transmitted to the gears such that C receives 60% and D receives 40%, figure 5. Determine the absolute maximum shear stress in the shaft
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