I have tried this problem a few different ways and still can\'t get it.... A uni
ID: 1344896 • Letter: I
Question
I have tried this problem a few different ways and still can't get it....
A uniform rod of mass 3.45×102 kg and length 0.380 m rotates in a horizontal plane about a fixed axis through its center and perpendicular to the rod. Two small rings, each with mass 0.250 kg , are mounted so that they can slide along the rod. They are initially held by catches at positions a distance 4.60×102 m on each side from the center of the rod, and the system is rotating at an angular velocity 27.0 rev/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?
Explanation / Answer
Here ,
let the final angular speed of the rod is wf
initial angular speed , wi = 27 rev/min
initial moment of inertia of system , I1 = M*L^2/12 + 2 * m * (4.6 *10^-2)^2
I1 = 3.45 *10^-2 * (0.38)^2/12 + 2 * 0.25 * (4.6 *10^-2)^2
I1 = 1.47 *10^-3 Kg.m^2
final moment of inertia of system . I2 = M*L^2/12 + 2 * m * (L/2)^2
I2 = 3.45 *10^-2 * (0.38)^2/12 + 2 * 0.25 * (0.38/2)^2
I2 = 1.84 *10^-2 Kg.m^2
as I1 * wi = I2 * wf
1.47 *10^-3 * 27 = 1.84 *10^-2 * wf
wf = 2.16 rev/min
the final angular speed of the system is 2.16 rev/min