A uniform 210 g rod with length 69 cm rotates in a horizontal plane about a fixe

Question

A uniform 210 g rod with length 69 cm rotates in a horizontal plane about a fixed, vertical, frictionless pin through its center. Two small 26 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 14 cm on each sides of the center, at which time the system rotates at an angular speed of 19 rad/s. Suddenly, 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

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)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.