A uniform 110 g rod with length 70 cm rotates in a horizontal plane about a fixe

Question

A uniform 110 g rod with length 70 cm rotates in a horizontal plane about a fixed, vertical, frictionless pin through its center. Two small 38 g beads are mounted on the rod such that they are able to slide without fric- tion along its length. Initially the beads are held by catches at positions 10 cm on each sides of the center, at which time the system rotates at an angular speed of 14 rad/s . Sud- denly, the catches are released and the small beads slide outward along the rod.
Find the angular speed of the system at the instant the beads reach the ends of the rod. Answer in units of rad/s.

Explanation / Answer

As angular momentum will be conserved.

Ii i = If f

(110 x 702 /12 + 2 x( 38 x 102 ) ) x 14 = (110 x 702 /12 + 2 x (38 x 352 )) x

52516.667 x 14 = 138016.667

= 5.33 rad/s

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