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## Main Question or Discussion Point

Hello people,

So i found out the tension in a ring rotating with constant angular velocity (in gravity free space)

Considering a small element of mass dm - tension will provide the centripetal force,

2Tsin(dθ/2) = dmrω^2

sindθ ≈ dθ

dm = m/2πr ds

ds = rdθ

T = (mrω^2)/2π

Now, the other method

K.E. = K = 1/2 Iω^2 = 1/2 mr^2 ω^2

If we increase the radius from r to r+dr, then work done by tension

dW = T d(2πr) = dK

T = 1/2π dK/dr

T = (mrω^2)/2π

Even though i get the same result, i have a doubt whether the second method is correct

I know that F=-dU/dr , but whether T=dK/ds , i don't know

Also, i want to know the general approach of calculating tension in situations like electro-magnetic fields, rotation & all.

Regards

So i found out the tension in a ring rotating with constant angular velocity (in gravity free space)

Considering a small element of mass dm - tension will provide the centripetal force,

2Tsin(dθ/2) = dmrω^2

sindθ ≈ dθ

dm = m/2πr ds

ds = rdθ

T = (mrω^2)/2π

Now, the other method

K.E. = K = 1/2 Iω^2 = 1/2 mr^2 ω^2

If we increase the radius from r to r+dr, then work done by tension

dW = T d(2πr) = dK

T = 1/2π dK/dr

T = (mrω^2)/2π

Even though i get the same result, i have a doubt whether the second method is correct

I know that F=-dU/dr , but whether T=dK/ds , i don't know

Also, i want to know the general approach of calculating tension in situations like electro-magnetic fields, rotation & all.

Regards

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