A 11-kg rod of length 800 mm can slide freely in the 240-mm cylinder DEwhich in

Question

A 11-kg rod of length 800 mm can slide freely in the 240-mm cylinder DEwhich in turn can rotate freely in a horizontal plane. In the position shown, the assembly is rotating with an angular velocity of magnitude = 40 rad/s and end B of the rod is moving toward the cylinder at a speed of 75 mm/s relative to the cylinder. Knowing that the centroidal mass moment of inertia of the cylinder about a vertical axis is 0.025 kg m2 and neglecting the effect of friction, detemine the angular velocity of the assembly as end B of the rod strikes end E of the cylinder. (Round the final answer to two decimal places.) 120 mm 320 mm 240 mm The angular velocity or the assembly is u2

Explanation / Answer

given m = 11 kg
l = 0.8 m
x = 0.24 m
wi = 40 rad/s
Vb = 75 mm/s

Ic = 0.025 kg m^2

intiial moment of inertia of the assembly = Ic + ml^2/12 + m(0.4 - 0.44)^2
Ii = 0.629266 kg m^2

final moment of inertia of the system = Ic + ml^2/12 + m(0.4 - 0.68)^2 = 1.474 kg m^2
hence form conservation of angular momentum
Ii * wi = If * wf
wf = 17.0756 rad/s

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