http://www.maths.qmul.ac.uk/~rpn/ASTM735/lecture3.pdf(adsbygoogle = window.adsbygoogle || []).push({});

The diagram on page 26 is the accretion disc.

The torque acting on the inner edge of the ring (the one that has a thickness of dR in the diagram) is

RF_{in}= -2[itex]\pi[/itex]R^{3}[itex]\nu[/itex]Ʃ[itex]\frac{dΩ}{dR}[/itex]

The torque acting on the outer edge of the ring is

RF_{out}= [2[itex]\pi[/itex]R^{3}[itex]\nu[/itex]Ʃ[itex]\frac{dΩ}{dR}[/itex]]_{R+dR}

I would think that the net torque acting would be

T = [2[itex]\pi[/itex]R^{3}[itex]\nu[/itex]Ʃ[itex]\frac{dΩ}{dR}[/itex]]_{R+dR}- [2[itex]\pi[/itex]R^{3}[itex]\nu[/itex]Ʃ[itex]\frac{dΩ}{dR}[/itex]]_{R}

= [2[itex]\pi[/itex]R^{3}[itex]\nu[/itex]Ʃ[itex]\frac{dΩ}{dR}[/itex]]dR

but according to equation (66) on page 27 of http://www.maths.qmul.ac.uk/~rpn/ASTM735/lecture3.pdf, the net torque is

[itex]\frac{∂}{∂R}[/itex][2[itex]\pi[/itex]R^{3}[itex]\nu[/itex]Ʃ[itex]\frac{dΩ}{dR}[/itex]]dR

Does anyone know why [itex]\frac{∂}{∂R}[/itex] is included in the expression?

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# Torque on the Accretion disc

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