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I'm trying to solve a problem where i have those three equations:

$TR= \frac{Ia}{R}$,

$mg-T = ma$,

I know that $I=\frac{7}{2}MR^2 $

I need to find the variable $a$. The solution of the problem says that:

$$a= \frac{2mg}{7M+2m}$$

I know that to find $a$ i need to solve a system, but i don't understand how it got to that solution. Can someone guide me through the step to get to that solution?

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2 Answers 2

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$T = (mg-ma) = m(g-a)$

and $I = \frac{7MR^2}{2}$

So, $TR = \frac{Ia}{R} \implies TR^2 = Ia \implies m(g-a){R^2} = \frac{7}{2}MR^2a$

$\implies 2mg-2ma = {7M}a\implies a (2m+{7M}) = 2mg $

$$a = \frac{2mg}{7M+2m}$$

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  • $\begingroup$ I understood! Thank you! $\endgroup$
    – Jack022
    May 31, 2019 at 17:13
  • $\begingroup$ You're welcome! $\endgroup$
    – 19aksh
    May 31, 2019 at 17:34
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But $$a=\frac{TR^2}{I}$$ and $$a=\frac{mg-T}{m}$$ so it must be $$\frac{TR^2}{I}=\frac{mg-T}{m}$$

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