As shown in the figure, ball 1 with m1=4.00 kg is connected through a mass less

Question

As shown in the figure, ball 1 with m1=4.00 kg is connected through a mass less rod with ball 2 with m2=3.00kg. The system is rotating at angular speed omega=8.00 rad/s about a vertical axle going through the center of the rod.

(a) How far away is the center of the mass of the system from the axle?
(b) Find the kinetic energy of the system. (l=mr^2 can be directly used to calculate the rotational inertia about the axle)
(c) What is the net force on each ball? (hint: try to apply F= m(v^2/r) and the relation between omega and v)

Thanks guys. If you could show work as well that would be awesome.

Explanation / Answer

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

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

Xcm = 3L/7, here L = length of the rod

b) K = (1/2)I2

= (1/2)(2 x mL2/4)(8)2

= 16mL2

c) F = ma

F1 = 4 x 2L/2

= 2 x 82 x L

= 128L N

F2 = 3 x 2L/2

= 96L N

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