328_Physics ProblemsTechnical Physics

328_Physics ProblemsTechnical Physics - 330 Angular...

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330 Angular Momentum P11.14 Fm a xx = T mv r sin θ = 2 a yy = Tm g cos = So sin cos = v rg 2 vr g = sin cos Lr m v mr g Lm g r r g = = = = sin . sin cos sin cos sin sin cos 90 0 23 4 A A , so m l FIG. P11.14 P11.15 The angular displacement of the particle around the circle is θω == t vt R . The vector from the center of the circle to the mass is then RR cos ± sin ± θθ ij + . The vector from point P to the mass is ri i j j =+ + F H G I K J F H G I K J + F H G I K J L N M O Q P R R vt R vt R ± cos ± sin ± cos ± sin ± 1 The velocity is v r F H G I K J + F H G I K J d dt v vt R v vt R sin ± cos ± So Lr v m Li j i j Lk + = F H G I K J + L N M O Q P mvR t t t t mvR vt R 1 1 cos ± sin ± sin ± cos ± ± cos ωω ω af x y m R P Q v FIG. P11.15 P11.16 (a) The net torque on the counterweight-cord-spool system is:
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