Exam 1 Practice Spring 2007 - R the vehicle P is heading...

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AAE 203, Spring 2007 Test One Problem 1 Determine whether or not the following equation is dimension- ally homogeneous. (a) mV ˙ γ = L - W cos γ + T sin α where L,W and T represent forces, m is a mass, V is a speed, and γ,α are angles. (b) What is the dimension of p in order for the following equation to be dimensionally homogeneous. m ¨ p + Ml sin( θ ) ˙ θ 2 = 0 where m,M are masses, l is a length, and θ is an angle. Problem 2 Consider the two pendulums of lengths a and b which are con- nected together and move in the ˆ e 1 - ˆ e 3 plane. Find nice expressions for e ¯ v P and e ¯ a P .
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Problem 3 Relative to the planet of radius
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Unformatted text preview: R , the vehicle P is heading north at a constant speed v . Relative to reference frame f , the planet is rotating at a constant rate ω about its N-S axis. Find nice expressions for f ¯ v P and f ¯ a P . Problem 4 The aircraft is pitching at a constant rate q relative the the earth. The propeller P is rotating at a constant rate ω relative to the aircraft. Find nice expressions for e ¯ ω P and e ¯ α P where e is Fxed in the earth....
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