Kinetic Energy of a Rotating Hoop - Physics Forum

Click For Summary

Homework Help Overview

The discussion revolves around the kinetic energy of a rotating hoop, specifically in the context of formulating the kinetic energy expression for use in the Lagrangian mechanics framework.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to formulate the kinetic energy expression for a rotating hoop, questioning if the expression T = \frac{1}{2} M a^2 w^2 is correct. Another participant prompts a consideration of the moment of inertia related to the setup.

Discussion Status

The discussion has progressed with participants exploring the formulation of the kinetic energy expression. There is an indication that the original poster's understanding has evolved, as they adjust their expression based on feedback.

Contextual Notes

Participants are discussing the kinetic energy in the context of Lagrangian mechanics, which may imply specific assumptions about the system's constraints and definitions.

rmfw
Messages
53
Reaction score
0
Hey PF, this is just a quick question:

If there's a hoop of mass M and radius a rotating around its vertical axis (see pic) and I want to write the kinetic energy for the Lagrangian is it just [itex]T = \frac{1}{2} M a^2 w^2[/itex] ? Considering w the angular velocity
 

Attachments

  • hoop.jpg
    hoop.jpg
    4.4 KB · Views: 445
Physics news on Phys.org
Not quite. What is the moment of inertia for this set up?
 
[itex]T =\frac{1}{2} w^2 \frac{1}{2} M a^2[/itex] ? is it more close to the answer now?
 
Yeah it's right now
 
  • Like
Likes   Reactions: 1 person

Similar threads

  • · Replies 21 ·
Replies
21
Views
5K
  • · Replies 33 ·
2
Replies
33
Views
3K
Replies
9
Views
3K
Replies
6
Views
1K
  • · Replies 8 ·
Replies
8
Views
1K
Replies
2
Views
1K
Replies
4
Views
1K
  • · Replies 16 ·
Replies
16
Views
1K
Replies
1
Views
2K