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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 disc with radius, R, rotates (at an angular speed of ?) near a surface that is fixed. The space between the disc and surface is filled with a fluid that has viscosity, µ. The distance between the disc and surface is h. Find the dependence between t..
Derive an expression for the determination of I of the disk about the g-g-axis in terms of the disk weight W, I, r, and the torsional period τ of small oscillations.
a worm gear set has a velocity ratio of 0.05. the worm has two teeth a lead of 3 in. and a pitch diameter of 1.5in.
If in Figure 4.8, instead of a knife-edge follower, a flat-faced follower is to be used, would the displacement diagrams for both designs be identical? And, if not, what would be the difference?
Energy in the home, personal energy use and home energy efficiency. Efficient use of ‘waste' heat and renewable heat sources.
in a stationary gas turbine engine ambient air at 100 kpa and 300 degrees k enters the adiabatic compressor. after
A steam power plant operates on a simple Rankine Cycle between the pressure limits of 10MPa and 50kPa. The mass flow rate of the steam is 50kg/s. The quality of the steam at the turbine exit is 90%.
A pitot-static probe attached to a manometer that has water as the manometer fluid is proposed as the measuring device for an airflow with a velocity of 8 m/s. What manometer reading is expected? Comment as to the use of the proposed device.
Which hexadecimal number has the greatest value? 10, C5, 9F, AE.
Assume that the coupler link is parallel to the frame link, and that the frame link is 10 cm, the coupler link is 7 cm, the link connecting the two jaws is 2 cm, and the fourth link is 3 cm. What is the angle by which the coupler link rotates from..
Recall bugs are the pain points that bother people, e.g., the BZ box Shark Tank video we saw during the lecture. Start from youself, what bothers you in your everyday life. Is your pain point likely shared by other people?
You have a container of gas with a molar volume of V¯=0.12 dm3·mol-1 at a temperature of T=280 K. You know that for this gas, 280 K corresponds to a reduced temperature TR=1.5 and that you are applying a reduced pressure of PR=4. Using your knowledge..
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