Three particles, each of mass 2.0 kg, are fastened to each other and to a rotati
ID: 1610200 • Letter: T
Question
Three particles, each of mass 2.0 kg, are fastened to each other and to a rotation axis by three massless strings, each 0.290 m long, as shown in the Figure. The combination rotates around the rotation axis with an angular velocity of 14.0 rad/s in such a way that the particles remain in a straight line.
1. What is the rotational inertia of the system?
2. What is the magnitude of the total angular momentum of the three masses?
3. If the outermost mass was to break free from the string, what would its linear momentum be?
Explanation / Answer
let m = 2 kg
r = 0.29 m
w = 14 rad/s
1) Rotational inertia of the system,
I = m*r^2 + m*(2*r)^2 + m*(3*r)^2
= 14*m*r^2
= 14*2*0.29^2
= 2.35 kg.m^2
2) angular momenumt, L = I*w
= 2.35*14
= 32.9 kg.m^2/s
3) linear speed of the outermost mass, v = 3*r*w
= 3*0.29*14
= 12.18 m/s
linear momentum of outermost mass, p = m*v
= 2*12.18
= 24.36 kg.m/s
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