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Not losing points on FBD

Free Body Diagrams (FBD) are generally the first and most important step in most physics problems; however, it's often the most points lost in a problem. with these guidelines, it should be easy.

Rules

1. Choose a coordinate system

• The most common is a cartesian coordinate system with the x-axis parallel with the ground, either horizontal or angled to match a sloped surface (see the block on a slope problem. every vector in the problem is in the same coordinate system.

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• A more interesting approach involves having a different coordinate system for each object in the problem, this is most useful in the Atwoods machine problem, as well as any other system where objects are tied together. It's most useful on problems with objects on 2 different sloped surfaces, where when released, one goes down the slope and the other is pulled up a different slope; defining one direction of motion as positive x allows for the acceleration (see newtons laws) to be a single common value in one direction and zero in the others.

• Polar coordinates are super useful in later chapters on rotational kinematics, but for now, a slice of time for a rotating object can be drawn in a cartesian coordinate system (see the banking turn problem). problems with a given magnitude and direction vectors (such as the air traffic control problem) can be best solved by turning the mag and direction polar coordinates into cartesian, where they can then be simply added together.

2. Do NOT put the acceleration or net force on the same drawing as the individual contributing forces. YOU WILL LOSE POINTS​

• if you really want to, have a separate drawing with the direction of motion/ net force only.

• have separate FBDs for each component even if they are in contact with each other (see the stacked block problem)​

3. Pretty pictures are sometimes ok.​

• Generally, I use a square or circle for the object, extra shading texturing takes time better spent on more physics (or going to bed early). I use the center of the shape for labeling what component (ABC, NOT numbers, greek letters, names) or just filling it in with the mass of the object.

• for any problems involving torque better drawings are nice, as the location of the force on the body is important.

• keep a straight edge handy for perpendicular lines and triangles. A clean drawing is better than a fancy one.

4.  Every force you can think of, magnitude, direction, and location.

• Gravity is always down (for problems on earth) applied to the center of mass, regardless of coordinate system, for the block on a slope problem with a rotated coordinate system, the most common mistake I see is gravity needs to have a component of its magnitude (using SOH CAH TOA) in both x and y-axes. I generally use "mg" or "W" for force-of-gravity and weight respectively. "F_g" is common, but beware of having too many F_?? subscripts leading to confusion ​

• Normal force is applied at the contact surface between two objects and is applied in equal magnitude with opposite directions onto both objects. I often use a "N_AB" as the normal force variable with the subscript denoting which 2 objects it refers to (objects "A" and "B"). Remember that it is always pointing away from the other object. The name "Normal" does not come from the word "regular", but the geometrical definition of a vector perpendicular to a surface. Assume positive magnitude, if the number goes to zero, the force does not exist, and a negative value would imply tension between the objects or they are moving apart. See the series of questions finding the maximum static value of a force such as the up a bump problem. Saying this again because it's important, if 2 objects are involved, the normal force acts in the opposite direction with the same magnitude on the 2nd object

• Friction force always opposes the direction of motion. It acts on a contact surface or point that has a normal force within the plane opposing direction of motion, meaning it always works to reduce the relative velocity between the 2 contacting objects. Because it is within the contact plane, it is always at a 90° angle to the normal force. Remember, it also has an equal and opposite force applied to the other object. the magnitude of the friction force is the normal force times a constant dependent on what materials are present, so "f = N_AB*µ". (I don't know how to use LaTeX in this editor) I usually use a curly f as the variable for handwritten work see example but F_f is a commonly used name instead (underscore means subscript (I hate this editor)). The weird symbol for the constant I mentioned earlier is called the coefficient of friction and is denoted with the greek letter µ spelled in English as mu and pronounced like a cat. Static and Kinetic friction both follow these rules, but the distinction deserves its own page

• Tension and compression are how force is transmitted within solid objects, and in the world of physics 1 and 2, is easily modeled as an equal and opposite force acting on 2 ends of the same object. later in higher engineering classes, these two are considered the same thing, and compression just has a negative value. But the ends of our theoretical ropes also have an equal and opposite force applied to whatever they are tied to (see the Atwoods machine problem). I usually use "T" for my tension variable, with subscripts noting what objects it connects. For problems with many tension forces and not many others (see the method of joints), I use the names of the 2 objects it connects "AB" with an overbar

• External a lot of problems have some externally applied force that is usually tension, normal, or something else in disguise. For external forces, you usually don't care about the equal and opposite forces, but note it does exist. The problem will usually say what direction it's applied, and the location is the center of mass (COM) unless otherwise specified. This is the one place I use an "F" as my variable, but if you know what it is, name your variables whatever's appropriate.

• Other common forces include lift (acts like normal force, see banking turn), drag (opposes the direction of motion), electric forces (acts like gravity) buoyancy (gravity but up)

5. Centrifugal force is real

• but not really, it's always ​another force in disguise such as the tension in the swinging bucket, gravity in orbits, or normal force or lift on the banking turn problem

• The centrifugal force you feel is the sum of forces required to give the circular motion described by centrifugal acceleration. Actually explaining why this happens is a bit of calculus explained here

• IT DOES NOT GO IN YOUR FBD, at least not separate from the disguised force

6. Turning a drawing into an equation ​

• This is worth a page on its own

• In short, Newton's 2nd law can be applied in each direction of the chosen coordinate system, where the acceleration in that direction can be found with F=ma and the sum of the components of every force in that direction.

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