Types of Forces in Free Body Diagrams
Mechanics runs on a short list of forces. Learn the direction rule for each and drawing a diagram stops being a judgement call.
Every force below has a fixed direction rule. Once you know which force it is, you know which way the arrow points.
The forces that belong
- WeightW, mg
- Straight down, drawn from the centre of gravity. W = mg, with g about 9.81 m/s².
- Normal forceN
- Perpendicular to the contact surface, pushing into the body. It can never pull.
- Frictionf
- Along the surface, opposing the sliding or the tendency to slide. f = μₖN when sliding, f ≤ μₛN when not.
- TensionT
- Along the rope, pulling away from the body. A rope only pulls.
- Spring forceFs
- Along the spring axis, back toward its natural length. Stretched springs pull, compressed springs push. Fs = kx.
- Applied forceF, P
- Exactly as the problem gives it. Resolve it into components along your axes when you write the equations.
- Distributed loadw
- A row of arrows over the loaded length, in N/m. For equilibrium, replace it with a single force equal to the area of the load, acting at its centroid.
- DragF_D
- Opposite the velocity of the body through the fluid. Ignored unless the problem says otherwise.
Two of these catch people out. Friction is not always backwards — for a car’s driving wheels, or a box on a truck bed that is speeding up, friction points forward, because it is what stops the surfaces slipping. And the normal force is rarely mg: on an incline it is mg cos θ, in an accelerating lift it is m(g ± a), and if a rope takes part of the load it is less than either.
What does not belong
Four arrows that get drawn and should not be:
- A “force of motion” — motion is what forces produce, not a force itself. Nothing pushes a sliding object along.
- Centrifugal force — circular motion needs a net force pointing inward, supplied by real forces like tension or friction. Nothing pulls the body outward.
- Internal forces — between parts of the same isolated body they cancel in pairs, so they never appear.
- ma — that is the other side of Newton’s equation, not a force acting on the body.
If you cannot name what is applying a force, it is not a force. Delete the arrow.
FAQ
Can the normal force be something other than mg?
Usually it is. On an incline N = mg cos θ; in an accelerating lift N = m(g + a); if a rope takes part of the weight, N is smaller than mg. Never assume N = mg without checking the vertical equation.
Is weight the same as mass?
No. Mass in kilograms is how much matter there is; weight in newtons is the gravitational force on it, W = mg.
Which way does tension point?
Always away from the body, along the rope. A rope can pull and cannot push. An ideal pulley redirects a rope without changing its tension, so the same T acts on both sides.