Force Diagrams

Weight ($W$): The gravitational pull of the Earth on an object, calculated as $W = mg$. It always acts vertically downwards toward the center of the Earth, regardless of the orientation of the surface the object is on.

Normal Reaction ($R$ or $N$): The contact force exerted by a surface on an object. It always acts perpendicular to the surface of contact.

Friction ($F$): A resistive force that occurs when two surfaces slide (or attempt to slide) across each other. It acts parallel to the surface and always in the direction opposite to the motion or intended motion.

Tension ($T$): A pulling force transmitted through a string, rope, or cable. It always acts away from the object being pulled.

Thrust: A pushing force, often from an engine or a solid rod. Unlike tension, thrust acts towards the object it is pushing.

Step 1: Isolate the Object: Clearly identify which object you are analyzing and represent it as a single point (particle) to simplify the geometry of the forces.

Step 2: Add Non-Contact Forces: Always start by drawing the weight vector ($mg$) acting vertically downwards from the particle.

Step 3: Identify Contact Points: Look for every point where the object touches something else (surfaces, strings, rods) and add the corresponding reaction, friction, tension, or thrust forces.

Step 4: Define a Coordinate System: Choose two perpendicular directions for analysis, such as horizontal/vertical or parallel/perpendicular to an inclined plane, to resolve forces into components.

Check the value of $g$: Always verify if the exam board requires $g = 9.8 \text{ m s}^{-2}$ or $g = 10 \text{ m s}^{-2}$. This choice dictates the precision of your final answer; for $g=9.8$, round to 2 significant figures, and for $g=10$, round to 1 significant figure.

Don't forget the Normal Reaction: A common mistake is omitting the reaction force when an object is on a surface. If there is contact, there is almost always a reaction force.

Inclined Planes: When an object is on a slope, remember that weight still acts vertically down, not perpendicular to the slope. You must resolve the weight into components parallel ($mg \sin \theta$) and perpendicular ($mg \cos \theta$) to the plane.

Sanity Check: Ensure that your arrows are pointing in the correct physical direction. For example, friction should never point in the same direction as the motion.