I need to understand why the sentence in brackets is true. Why does the x component of weight contain a sine and y contain a cosine? The X-axis appears to be adjacent to 30 degrees.

Chapter 34 - Rolling without Slipping Examples Determine the acceleration of a solid sphere as it rolls without slipping down 30 incline. mg 30 Since the problem asks for acceleration, we should sum the components of the forces a the torques. Draw and label an extended FBD for the solid sphere. This means to draw the shape of the object and draw each force where it effectively acts on the object (Chapter 33) Weight pulls downward, normal force pushes perpendicular to the surface, and friction pushes up the incline (Although the problem didn't explicitly mention friction, it's implied since the solid sphere "rolls without slipping ") As we learned in a similar example in Chapter 14, the x-component of weight has a sine since x is opposite to 30", while the y. component of weight has a cosine since y is adjacent to 305. See page 135. Friction is the only force that exerts a torque (since the other forces point to or from the axis of rotation) The moment of inertia of a solid sphere is / = = mR (Chapter 32). [= = max . [6 = may . [ = la my sin 30 - f = max . N - mg cos 309 =0 . Rf sin 909 = = mAza Use the substitution a, = Ra: Rf sin 90 = = mRa, 2 f = = max Plug this equation in for friction in the x-sum: mg sin 30 - f = ma ing sin 30 -- 2 -max = ma, = ax tay = (#+ 1) as = (+3 )ax = 5as 5 5 5(9.81) 5(10) 149 25 14 14 - m/s