Moment of inertia changes during rotation -- Calculate work?

[Gian_ni]

Hi everyone, i have a question

Moment of inertia changes during rotation. Calculate the work that changes kinetic energy?
Angular moment (along the axis of rotation) L = I * w
A point mass M rotates along an axis attached to a mass-negligible rod, of length r.
If someone moves the mass M at distance r / 2, the angular moment must conserve ( so
L1 = I2 w2 -> w2 = 4w1) , but kinetic energy is changed: ΔK = 0.5M (w2 ^ 2 * (r / 2) - w1 ^ 2 * r) = 0.5M * w1 ^ 2 * 7r
Since the work performed by the internal force (?) has increased, ΔK = W is positive.
- But what force in this case did the work and during which displacement?
- Is there a way to calculate the Work W without the work-energy theorem? Calculations?

Thank you

 

[jambaugh]

Please submit HW questions in the Homework and Coursework Questions forum and read the guidelines before submitting.

 

[Gian_ni]

Please submit HW questions in the Homework and Coursework Questions forum and read the guidelines before submitting.

Thank you for reply. I''ll post, though it's not an homework but a ''problem'' made by myself to understand.

 

[berkeman]

Here is a link to the re-posted thread in the schoolwork forums:

https://www.physicsforums.com/threa...hanges-during-rotation-calculate-work.923137/