Question

How can I derive the first equation to get the second equation?

Answer 1

To derive the second equation from the first equation, you can substitute the expression for the unknown in terms of the other known variables. This reduces the equation to one unknown.

Step-by-step explanation:

To derive the second equation from the first equation, you need to substitute the expression for T₂ in terms of T₁. This will reduce the unknowns in the equation to one. Here are the steps:

1. Start with the equilibrium equation for the problem.
2. Substitute the expression for T₂ in terms of T₁ into the equation.
3. This will eliminate one unknown and result in a new equation with only one unknown left.

Answer 2

keeping in mind that "R" and "r" are constants whilst "s" is a variable and θ is a function in terms of "s", thus


`\bf s^2=R^2+r^2-2Rrcos(\theta )\implies 2s^1=0+0-2Rr\left[ \stackrel{chain~rule}{-sin(\theta )\cfrac{d\theta }{ds}} \right] \\\\\\ 2s=2Rrsin(\theta )\cfrac{d\theta }{ds}\implies 2s=\cfrac{2Rrsin(\theta )d\theta }{ds}\implies \cfrac{2s\cdot ds}{2Rr}=sin(\theta )d\theta \\\\\\ \cfrac{s\cdot ds}{Rr}=sin(\theta )d\theta`