A uniform rod of mass 2.65x10^-2kg and length 0.450m rotates in a horizontal pla

Question

A uniform rod of mass 2.65x10^-2kg and length 0.450m rotates in a horizontal plane about a fixed axis through its center and perpendicular to the rod. Two small rings, each with mass 0.160kg , are mounted so that they can slide along the rod. They are initially held by catches at positions a distance 5.40x10^-2m on each side from the center of the rod, and the system is rotating at an angular velocity 28.0rev/min . Without otherwise changing the system, the catches are released, and the rings slide outward along the rod and fly off at the ends.

What is the angular speed of the system at the instant when the rings reach the ends of the rod?

What is the angular speed of the rod after the rings leave it?

Explanation / Answer

We will treat the rings as point masses
Initially the moment of the system is
0.0265*0.45^2/12+2*0.16*0.054^2
I=0.0013

When the rings are at the very end of the rod the moment is
0.0265*0.45^2/12+2*0.16*0.2^2
I=0.01324

about 10X greater

Set up the momentum equation

0.0013*28=0.01324*w
solve for w

w=0.0013*28/0.01324

2.74 rev/min

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