Question

Three masses of mass M=1.2kg are initially located at positions:
r1→=4.0m i+2.8m j −4.4mk
r2→=5.4m i+1.0m j^+2.3m k
r3→=−2.6m i^−1.9m j^+2.0m k

The masses are held in place relative to each other by rigid, massless, rods which connect them to the z-axis. They begin to rotate around the z-axis with constant angular speed. If the system has angular momentum L⃗ =3597 what is the angular speed of the rotation? Answer in radians per second.

Answer 1

let M1 = M2 = M3 = M = 1.2 kg

distance from z axis to M1, r1 = sqrt(4^2 + 2.8^2) = 4.883 m

distance from z axis to M2, r2 = sqrt(5.4^2 + 1^2) = 5.492 m

distance from z axis to M3, r3 = sqrt(2.6^2 + 1.9^2) = 3.220 m

Moment of inertia of the system about z axis, I = M1*r1^2 + M2*r2^2 + M3*r3^2

= M*(r1^2 + r2^2 + r3^2)

= 1.2*(4.883^2 + 5.492^2 + 3.22^2)

= 77.2 kg.m^2

now use, L = I*w

==> w = L/I

= 3597/77.2

= 49.6 rad/s <<<<<<<<<---------------------Answer