Beaded Friction Catch
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Find the angular speed of the system at the instant the beads reach the ends of the rod. Answer in rad/s?
A uniform 210 g rod with length 58 cm rotates
in a horizontal plane about a fixed, vertical,
frictionless pin through its center. Two small
44 g beads are mounted on the rod such that
they are able to slide without friction along
its length. Initially the beads are held by
catches at positions 13 cm on each sides of the
center, at which time the system rotates at
an angular speed of 27 rad/s . Suddenly, the
catches are released and the small beads slide
outward along the rod.
use conservation of angular momentum according to which
I1 w1 = I2 w2, where w2 is the final angular speed of rod
( ml^2 /12 + 2 m1 r1^2 0 w1 =(ml^2 /12+2m1r2^2 )w2 ,where
m=210 gm, m1 = 44 gm, r1 = 13 cm, r2 = 29 cm, w1 = 27 rad/sec
subsitituting these values, and simplifying you can get
final angular speed w2 = 14.98 = 15 rad/sec (nearly)
( r1 is initial distance of beads from axis of rotation and r2 is the final distance after displacement)
