a student holds a 3.0kg mass in each hand while sitting on a rotating stool. when his arms are extended horizontally, the masses are 1.0m from the axis of rotation and he rotates with an angular speed of 0.75 rad/s. if the student pulls the masses horizontally to 0.30m from the axis of rotation, what is his new angular speed

Explanation:

Due to change in the position of 3 kg mass , the moment of inertia of the system changes , due to which angular speed changes  . We shall apply conservation of angular momentum , because no external torque is acting .

Initial moment of inertia I₁ = M R² = 3  x 1 ² = 3 kg m²

Final moment of inertia I₂ = M R² = 3  x .3 ² = 0.27  kg m²

Applying law of conservation of angular momentum

I₁ ω₁ = I₂ ω₂

Putting the values ,

3 x .75 = .27 x ω₂

ω₂ = 8.33 rad / s

New angular speed = 8.33 rad /s .

i'm thinking more like energy