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By A. Frank D'Souza

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Mt + fgmz ~ 60 Dynamics of Particles: Newton's Law, Energy, and Momentum Methods Sec. 5 Chap. 52) o The spring force is conservative. If the spring is stretched by an amount from its unstretched length, the spring force is F = -klJ, where k is the spring constant and it is assumed that the spring is linear. 16 Mechanism for shooting plunger. 50) a; t · dr Uz e e The negative sign in the foregoing equation is employed so that if the work is positive, the potential energy decreases, and vice versa.

3 Case 3: 0 < e < I, -[G(m 1 + m 2 )] 2j2h 2 < E < 0. The orbit is an ellipse. _ vz 2 a- G(m 1 + m2) v~ = and ra « where m 1 and m 2 are the masses of the satellite and earth, respectively. Since m 1 m 2 , m 1 + m 2 ~ m 2 and the equivalent mass of the satellite becomes m 1 m 2 /(m 1 + m 2 ) ~ m 1 , which is its actual mass. Eliminating va for the circular orbit, we obtain + ,+ mz)J'/2 71 to a malfunction of the control, the satellite is not projected horizontally but at an angle a: to the horizontal and, as a result, is projected into an elliptic orbit.

W»IF X ; + w X ;) dm. 21) is modified as and Ixz = Izx = -I XZ dm H,! Hy Sec. 3 rn = = [I. (sin 11. )} 0 m(/crR2 + ~hZ)co. cos 11. t•'J Dynamics of Rigid Bodies: Newton's Law, Energy, and Momentum Methods 88 Chap. 4 Sec. 3 Linear and Angular Momentum of a Rigid Body 89 (b) The linear and angular momentum of the cone are now obtained by employing a coordinate system whose origin is at the mass center C and whose angular velocity is again W= OJ 0 sin fXf + OJ0 cos rxk zl as shown in Fig. 5. 6 Parallel axes theorem.

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