a&w restaurant: In a free body diagram, can you leave a force at, say, a 30 degree angle, or would you break that up into x and y components?|||In case of angle we need to break the force into their x and y components. Suppose any force F makes 30 degree with horizontal , then, its x-component (or, horizontal component) = F cos30 And, y-component (or, vertical component) = F sin30|||no, break it using the sin and cos f(x)s. say F=10N, making angle 30deg with horizontal. Then, horizontal force (Fx)=Fcos 30 and vertical force (Fy)= Fsin 30.|||You can absolutely leave a force vector at an angle. However, it is often easier to ADD UP all the force vectors if you express them all as components that are all parallel or perpendicular to each other. That is really the whole reason for breaking into components; so you can do the whole vector sum in terms of two equations, one equation comparing components along one axis, and the other equation comparing components along the other axis. Depending on the problem, sometimes it's more convenient to break them into horizontal and vertical components, and sometimes it's more convenient to break them into coordinate axes that are tilted. For example, when dealing with motion along a ramp, you usually choose to break your vectors into components that are parallel and perpendicular to the RAMP; that's because you know that the motion is confined to the "upslope/downslope" line (i.e. parallel to the ramp), and therefore you know that vectors components of force, velocity, acceleration, etc. that are PERPENDICULAR to the ramp must add up to zero, which can make your total calculation simpler. While in other types of problems, it may be more convenient to use horizontal and vertical components. Note that it's not "wrong" to use components in any direction you choose -- for example, if you want to use horizontal/vertical components in a ramp problem, you'll still get the right answer. But you may find that you have to do more math to get there.