(Extra Credits 5\') As shown in the figure, ball 1 with m1 = 4.00 kg is connecte

Question

(Extra Credits 5') As shown in the figure, ball 1 with m1 = 4.00 kg is connected through a mass less rod with ball 2 with m2 = 3.00 kg. The system is rotating at angular speed omega = 8.00 rad / s about a vertical axie going through the center of the rod. How far away is the center of the mass of the system from the axie? Find the kinetic energy of the system. can be directly used to calculate the rotational inertia about the axie) what is the net force on each ball? (hint: try to apply F = m v2/r) and the relation between omega and v)

Explanation / Answer

a) (m1 + m2)Xcm = m1x1 + m2x2

(4 + 3)Xcm = 4(0) + 3(L)

Xcm = 3L/7

distance of the centre of rod from centre of mass = L/2 - 3L/7

d = 0.0714L

b) I = m1L2/4 + m2L2/4

I = L2/4[m1 + m2]

I = 7L2/4

I = mL2/2

K = (1/2)I2

K = (1/2)(7L2/4)(82)

= 56L2

c) net force = m12L/2 = 4 x 8 x 8 L/2 = 128L

on m2, = 3 x 8 x 8 x L/2 = 96L

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