# Resolving the forces into components [closed]

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? 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?

• Am I missing the question? Isn't it N*cos(theta)?
– r13
May 7 at 14:02
• 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 ? May 7 at 15:58

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,

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

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

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!

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