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okay so I am really struggling to see how to resolve the Normal reaction force and Weight into the r and theta direction please? Why is it that the angle is taken to the left of N and right of mg please?enter image description here

Can someone give me some tips on this please? And why isn’t the N force resolved with the angle to the right of it attached to the theta line please?

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  • $\begingroup$ Am I missing the question? Isn't it N*cos(theta)? $\endgroup$
    – r13
    May 7 at 14:02
  • $\begingroup$ Hi, so I just don’t get why the N and mg are resolved like that, could it be done y resolving against the theta axis too please ? $\endgroup$
    – Emmaneulle
    May 7 at 15:58
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You need to review the trigonometric functions. In your question, assume the forces are to be resolved into component forces along the orthogonal axes r & q,

$\sum F_r = Rcos\theta - Ncos\theta = (R-N)cos\theta$

$\sum F_q = F + Rsin\theta - Nsin\theta = F + (R-N)sin\theta$

enter image description here enter image description here

If you have any doubt, you can prove the validity of the component forces by the "rule of the right triangle":

$c^2 = a^2 + b^2$, thus

$R = \sqrt{R^2sin^2\theta + R^2cos^2\theta} = \sqrt{R^2(sin^2\theta + cos^2\theta)}= \sqrt{R^2} = R$, CHECK!

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  • $\begingroup$ Hi r13, thank you very much. $\endgroup$
    – Emmaneulle
    May 7 at 18:26
  • $\begingroup$ You are welcome. $\endgroup$
    – r13
    May 7 at 18:27

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