Moment of inertia changes during rotation -- Calculate work?

AI Thread Summary
The discussion focuses on calculating the work done when the moment of inertia changes during rotation, specifically when a point mass is moved closer to the axis of rotation. It establishes that while angular momentum is conserved, the kinetic energy changes, leading to a positive work done by internal forces. The poster seeks clarification on which force performs this work and the displacement involved. Additionally, they inquire about alternative methods to calculate work without relying on the work-energy theorem. The conversation emphasizes understanding the relationship between moment of inertia, angular momentum, and kinetic energy changes in rotational dynamics.
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
 
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Please submit HW questions in the Homework and Coursework Questions forum and read the guidelines before submitting.
 
jambaugh said:
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.
 

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