Torsional spring and maximum velocity of wheel

AI Thread Summary
The discussion focuses on solving a problem involving a torsional spring and the maximum velocity of a wheel using energy conservation principles. Participants agree that the energy transfer occurs from the spring to the wheel as long as the torque from the spring remains positive. The conversation highlights that the wheel will continue to accelerate until the net rotation ceases, at which point all potential energy from the spring is converted into kinetic energy of the wheel. Calculus is deemed unnecessary for this analysis, as the energy transfer can be understood conceptually. The thread emphasizes the relationship between spring potential energy and wheel kinetic energy in determining maximum velocity.
surya teja saithana
h
Moderator's Note: HOMEWORK POSTED IN WRONG THREAD, SO NO TEMPLATE
Thread title changed to make it descriptive of the problem.

media%2Fdf7%2Fdf764b9c-d73b-4777-9eb1-f1b97d2073ec%2Fimage.jpg

can i solve this question using energy conservation method as shown.
media%2Faf5%2Faf5a2873-1544-4dbb-9333-ef4376d51b80%2Fphpvs8w6i.png

media%2F700%2F70086f40-8147-41bb-ae7e-a3d61e33c41a%2FphprgjoBs.png
 
Last edited by a moderator:
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Your work and result look good to me.

I would probably have skipped the calculus myself, realizing that the wheel would be accelerating so long as the torque applied by the spring was positive and so transferring energy from the spring to the wheel. Hence the energy transfers from the spring to the wheel until the net rotation returns to zero, whereupon all the spring PE has moved to the wheel KE.
 

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