Why is it the only force? I wonder there is mgsin that is exactly opposite direc

Question

Why is it the only force? I wonder there is mgsin that is exactly opposite direction of frictional force Why that is not considered? *i asked this problem before but mistakenly i confused so i said mgcos but why i wanna know is mgsin Figure 8.6.1 Body rolling down an Body Rolling Down an Inclined Plane As an thustration of laminar motion weStady the motion of a round object ( andso on) rolling down an inclined plane. As shown in Figure threeforcese on the body. These are (1) the downward force of gravity, (2) the normal plane Fs,and (3) the frictional force parallel to the plane F Choosing aes a the component equations of the translation of the center of mass are5 as (8.63 (8.64) where is the inclination of the planetitehorizontal. Because the contact with the plane, we have y, constant (8.65a) Hence, (8.65b) Therefore, from Equation 8.6.4, (8.66) The only force that exerts a moment F, The magnitude of this moment is Fra, where a is the raci's of the body rotational equation (Equation 8.6.2) becomes center of mass is the frictional force the (8.6.7) To discuss the problem further we need to make some assumptions (eo for two the equations of motion for two contact between the pane cases the We solve

Explanation / Answer

The acceleration of the center of mass is zero so the two forces acting on the object's center of mass must counter each other (or) they should balance each other.

So using this balance in the equation 8.6.4 we have normal reaction equal to mgcos(theta)

So the above set of equations are relevant for the y component of displacement and forces

when we talk about the x components of the forces, the first one is the frictional force denoted here by Fp which is present in the 8.6.3 and it is in addition to sin term.

so Fp=mg sintheta

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