(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Determine the kinetic energy of a bead of massmwhich slides along a frictionless wire bent in the shape of a parabola of equationy=x^{2}. The wire rotates at a constant angular velocity[tex]\omega[/tex]about they-axis.

2. Relevant equations

T = [tex]\frac{1}{2}[/tex]m([tex]\dot{x}^2[/tex] + [tex]\dot{y}^2[/tex] + [tex]{x}^2[/tex][tex]\omega^2[/tex])

3. The attempt at a solution

The above equation represents my attempt to write down the kinetic energy of the system in an appropriate coordinate system. After this I eliminated [tex]\dot{y}[/tex] in favour of [tex]\dot{x}[/tex] usingy=x^{2}and got:

T = [tex]\frac{1}{2}[/tex]m([tex]\dot{x}^2[/tex] + 4[tex]{x}^2[/tex][tex]\dot{x}^2[/tex] + [tex]{x}^2[/tex][tex]\omega^2[/tex])

Does this look right to anyone? The book (study guide) I'm using was unfortunately compiled by my University and no answers are supplied to end-of-chapter problems. This problem comes out of the first chapter of my study guide and all the problems there basically involves writing down a correct expression for the Lagrangian/Kinetic Energy.

Thanks in advance for any help.

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# Homework Help: Lagrangian mechanics: Kinetic energy of a bead sliding along a bent wire

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