Moment of inertia changes during rotation -- Calculate work?

• Gian_ni
In summary, the conversation discusses the concept of moment of inertia changing during rotation and how to calculate the work that changes kinetic energy. The formula for angular moment along the axis of rotation is mentioned, as well as an example involving a point mass rotating along a rod. The relationship between angular momentum and kinetic energy is explained, with the conclusion that the work performed by an internal force will result in a positive change in kinetic energy. The conversation ends with a question about how to calculate the work without using the work-energy theorem.
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

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.

1. What is moment of inertia?

Moment of inertia is a physical property of a rotating object that describes its resistance to changes in rotational motion. It is often referred to as the rotational equivalent of mass.

2. How does moment of inertia change during rotation?

Moment of inertia can change during rotation if the distribution of mass in the object changes. For example, if an object extends its arms or legs during rotation, it will have a larger moment of inertia compared to when its limbs are close to its body.

3. How is work calculated for changes in moment of inertia during rotation?

The formula for calculating work for changes in moment of inertia during rotation is W = 1/2 * I * (ωf^2 - ωi^2), where W is work, I is moment of inertia, and ωf and ωi are the final and initial angular velocities, respectively.

4. Can moment of inertia be negative?

No, moment of inertia cannot be negative. It is always a positive value that depends on the mass distribution and axis of rotation of an object.

5. How does moment of inertia affect the rotational motion of an object?

The moment of inertia affects the rotational motion of an object by determining how much torque is needed to produce a certain amount of angular acceleration. Objects with larger moments of inertia will require more torque to rotate, while objects with smaller moments of inertia will be easier to rotate.

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