The rotating systems shown in the figure differ only in that the two identical m

Question

The rotating systems shown in the figure differ only in that the two identical movable masses are" positioned a distance r from the axis of rotation (left), or a distance r/2 from the axis of rotation (right). You release the hanging blocks simultaneously from rest, and call t_L the time taken by the block on the left and t_R the time taken by the block on the right to reach the bottom, respectively. The bar, pulley, and rope have negligible mass, the rope does not slip, and there is no friction in the axle of the pulley. Under these conditions A) t_L = 1/2 t_R. B) t_L = t_R. C) t_L = Squareroot 2 t_R. D) t_L = 2t_R. E) t_L = 4t_R. A 10.0-kg uniform ladder that is 2.50 m long is placed against a smooth vertical wall and reaches to a height of 2.10 m, as shown in the figure. The base of the ladder rests on a rough horizontal floor whose coefficient of static friction with the ladder is 0.800. An 80.0-kg bucket of concrete is suspended from the top rung of the ladder, right next to the wall, as shown in the figure. What is the magnitude of the friction force that the floor exerts on the ladder A) 538 N B) 706 N C) 1290 N D) 833 N E) 601 N A 5.0-m radius playground merry-go-round with a moment of inertia of 2000 kg middot m^2 is rotating freely with an angular speed of 1.0 rad/s. Two people, each having a mass of 60 kg, are standing right outside the edge of the merry-go-round and step on it with negligible speed. What is the angular speed of the merry-go-round right after the two people have stepped on? A) 0.20 rad/s B) 0.40 rad/s C) 0.60 rad/s D) 0.80 rad/s E) 0.67 rad/s

Explanation / Answer

4) B) 0.4 rad/s

given

I = 2000 kg.m^2

r 5 m

wi = 1 rad/s

m = 60 kg

wf = ?

Apply conservation of angular momentum,

final angular momentum = initial angular momentum

If*wf = Ii*wi

wf = Ii*wi/If

= I*wi/(I + 2*m*r^2)

= 2000*1/(2000 + 2*60*5^2)

= 0.4 rad/s

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