Question

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Consider the system shown below. Each horizontal rod has a linear mass density of 1 kg per meter, and each vertical rod has a negligible mass. a. What mass for object A will balance the A-B system? What mass for object C will balance the whole system? b. Use the additive nature of moment of inertia and the parallel axis theorem to calculate the total moment of inertia of the entire system relative to the X. Take the moment of inertia for a rod rotating about its end to be 1-(1/3)MR2 c. If the system begins at rest, and a force of 10 N were applied horizontally to object C for 4 seconds, what would the resulting angular velocity be? Assume objects A and B do not rotate about their own center. d. If object B then fall off the system, what would the final angular velocity be? 0.6 m 0.3 m 0.4 m 0.5 m C A B = 2 kg

Answer 1

Sol GDE Density oliqa rod = m = 1 kg of Horizontal we Know from principle of Balance studursa fo Izglu zu 226 ire ma xo. 4 + 0,4 xi X0.2 • 4x1 toj 0-25 2x0,5 +0:5*1*.05 P isx Centre of mass 1 + 0.125 centre of 0,4 mA + 0,08 0.4 mA 1.045 Que k = 2.61 kg ~ 2.6 kg ? ? ma 'A 2.6 kg mass left side 206+ 2 +0,9 = m = 5.5kg 5.5 x 0.6 + 016*1 x Oje? me X0,3 + 0.3x1x0,15 Centre of maps 3.3 + 0,18 0.3 mc +0.045 0.3mc = 3.435 » mc= 11.5kg ow 11.5 kg 7 (b) بعيد r 11.5 +0.3 - 11.8 kg 2 Ix = 5.5 kg ; ma = m016)? + (0.632 mp (0.3) wi- 0 16 C + 0.3 (0.32 3 = *5.5 * 016 X0:6 +{ *11.8*0.3 70.3 2 x 0.600.600.6 + 0.370.3x03 Suomi 0.990+ 0.531 +0.072 + 0.009 I 1.683 kg-m² + 2 고 х

(©) f = ION d = 0.3 m from с To mass . have Y = F xd Id d = f d 10 x 0.3 । 1,683 & = 1.78 rad 2ی (d) have 2 lat? wt + E + lola 1.78 رها) * د لا ă x 16 x 1.78 8 x1-78 14.2 rad is Angular velocity 14.2 rad rad