0.3411.33 points I Previcus Arewers Ser SE7 11.P034 My Notes A uniform rod of ma

Question

0.3411.33 points I Previcus Arewers Ser SE7 11.P034 My Notes A uniform rod of mass 312 g and length 50 cm rotates in a horizontal plane about a fixed, vertical, frictionless pin through its center. Two small, dense beads, esch of mass m, are mounted on the rod so that they can slide withaut friction along its length Initially the beads are held by catches at positions 10 cm on each side of center, and the system is rotating at an angular speed of 39.0 rad/s. The catches are released simultaneously, and the small beads slide outward along the rod. (a) Find the angular speed wr of the system at the instant the beads side off the ends of the rod as it depends on m. (Use m as necessary.) rad/s (b) What is the maximum value for r when m 0? x rad/s what is the minimum value for , as m approaches infinity? rad/s

Explanation / Answer

(A) Ii = m L^2 / 12 + 2 ( M d^2)

Ii = (0.312 x 0.50^2 / 12) + 2( m (0.10^2))

Ii =0.0065 + 0.02m

If = m L^2 / 12 + (2 m 0.25^2) =0.0065 + 0.125m

Applying angular momentum conservation,

Ii wi = If wf

(0.0065 + 0.02m)(38) = (0.0065 + 0.125m ) wf

wf = ((0.0065 + 0.02m)/(0.0065 + 0.125m )) (38)

.........Ans

(b) when m = 0 then wf = 38 rad/s

(c) ((0.0065/m + 0.02) / (0.0065/m + 0.125))(28)

when m is infinity then 0.0065/m + 0.02 = 0.02

and 0.0065/m + 0.125 = 0.125

wf = 0.02 x 38 / 0.125

wf =6.08 rad/s

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