here,
the mass of each rod , m = 6 kg
the length of rod , l = 1 m
a)
the moment of inertia of this object , I0 = (m * l^2 /3) + m * l^2
I0 = 6 * 1^2 * (1/3 + 1) kg.m^2
I0 = 8 kg.m^2
b)
w0 = 4 rad/s
using Work-energy theorm
work done needed , W = change in kinetic energy
W = 0.5 * I0 * w0^2
W = 0.5 * 8 * 4^2 J = 64 J
c)
let the final angular velocity be w
using conservation of angular momentum
I0 * w0 = I * w
(m * l^2 /3 + m * l^2) * w0 = ( m * (2l)^2 /3) * w
(4/3 * m * l^2) * w0 = (4/3 * (2 m) * (l)^2) * w
w = w0 /2 = 2 rad/s
the final angular velocity will be 2 rad/s
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