This is from Dynamics where r(dot) is the time derivative of the radius.(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\dot{r} = \frac{d(r)}{dt}[/tex]

[tex]\dot{r} = \frac{d}{dt}(2R\sin(\frac{\theta}{2})) \ \ \ \ \ \mbox{note: this is given}[/tex]

[tex]\dot{r} = 2R\frac{d}{dt}(\sin(\frac{\theta}{2}))[/tex]

[tex]\dot{r} = 2R\cos(\frac{\theta}{2})\frac{d}{dt}(\frac{\theta}{2})[/tex]

[tex]\dot{r} = 2R\cos(\frac{\theta}{2})(\frac{1}{2})\dot{\theta}[/tex]

[tex]\dot{r} = R\dot{\theta}\cos(\frac{\theta}{2})[/tex]

I am confused on one part...in this step:

[tex]\dot{r} = 2R\frac{d}{dt}(\sin(\frac{\theta}{2}))[/tex]

[tex]\dot{r} = 2R\cos(\frac{\theta}{2})\frac{d}{dt}(\frac{\theta}{2})[/tex]

Why do you have to differentiate the sin(theta/2)?? Since you are differentiating with respect to t, don't you count the theta as a constant and therefore not differentiate it? But my profressor said that the above is correct.

PS: Sorry for my bad tex.

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# Homework Help: Calculating r(dot)

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