Posted on January 11, 2010.
and kinetic energy problem of angular velocity? A heavy, circular merry-go-round has a radius of 1.5 m and a moment of inertia (about its central axis) of 350 kgm ^ 2.
Four children act simultaneously with four different forces on the edge of the Merry-go-round:
One child: 450 N, clockwise, tangential
Child B: 620 N, counter-clockwise, tangential
Child C: 350 N, just outside the center
Child D: 550 N, counterclockwise at an angle of 120 ° from the center
A) Find the net resultant torque on the merry-go-round. Will the CW or CCW? (Assume that the axis of the Merry-go-round is no friction.) (Image: http://hphotos-snc3.fbcdn.net/hs367.snc3/23626_1400055846547_1386835711_1082873_4858020_n.jpg)
Thanks to the summation of all couples, I ÎŁT = + + + T_a T_b T_d T_c = 2319 Nm
But I do not know how to determine CW or CCW. Which is it?
B) b) Suppose that later the same merry-go-round has no outside torques acting on it. Some children are riding on the carousel near its edge, giving the whole system a moment of inertia initial total of 650 kgm ^ 2. He turns to the initial angular velocity of 2.0 rad / s. The children then migrate to the center of the merry-go-round, reducing the time the inertial system to a final value of 450 kgm ^ 2. What will be the final Merry-go-round of the angular velocity?
I found this part of the conservation of angular momentum.
(Iω) _i = (Iω) _f
solve for me _f ω 2.89 rad / s
That is my answer correct?
C) Find the change of system kinetic energy during the Part B, if applicable.
k_rot = (0.5Iω ^ 2) _f - (0.5Iω ^ 2) _i = 0.5 (650kgm ^ 2) (2.89 rad / s) ^ 2 - 0.5 (450kgm ^ 2) (2.0rad / s ) ^ 2 = 1814 J
That is my answer correct?
