Answer:
The angular speed of the system at the instant the beads reach the ends of the rod is 14.87 rad/s
Explanation:
Moment of inertia is given as;
I = ¹/₁₂×ML² + 2mr²
where;
I is the moment of inertia
M is the mass of the rod = 0.19 kg
L is the length of the rod = 0.43 m
m is the mass of the bead = 0.038 kg
r is the distance of one bead
Initial moment of inertial is given as;

Final moment of inertia is also given as

Angular momentum is the product of angular speed and moment of inertia;
= Iω
From the principle of conservation of angular momentum;


Given;
ωi = 12 rad/s
r₁ = 10.0 cm = 0.1 m
r₂ = 10.0cm/4 = 2.5 cm = 0.025 m
Substitute these values in the above equation, we will have;

Therefore, the angular speed of the system at the instant the beads reach the ends of the rod is 14.87 rad/s