Newton's First Law of Motion

• The Concept of Equilibrium: An object is in a state of equilibrium when the vector sum of all forces acting upon it is zero, expressed as $\sum \vec{F} = 0$. In this state, the object experiences no acceleration, meaning its velocity is constant.

• Vector Summation: Forces are vectors, meaning they have both magnitude and direction. To determine the net force, one must resolve all individual force vectors into their components (usually $x$ and $y$) and sum them independently.

• Inertial Reference Frames: Newton's First Law only holds true in reference frames that are not accelerating. If a reference frame is rotating or accelerating, 'fictitious forces' appear to act on objects, which can make it seem like the law is being violated.

• Identifying All Forces: To apply the law, first identify every interaction the object has with its environment, such as contact forces (friction, tension, normal) and long-range forces (gravity, magnetism).

• Constructing Free-Body Diagrams: Draw the object as a simplified point or box and represent every force acting on it as an arrow pointing away from the center. The length of the arrow should roughly represent the force's magnitude.

• Applying the Equilibrium Condition: If the problem states the object is at rest or moving at a constant velocity, set the sum of forces in each dimension to zero: $\sum F_x = 0$ and $\sum F_y = 0$. This allows for the calculation of unknown forces like friction or tension.

Static vs. Dynamic Equilibrium

• Mass vs. Weight: Mass is an intrinsic property representing the amount of matter and inertia, measured in kilograms. Weight is the force of gravity acting on that mass ($W = mg$) and varies depending on the local gravitational field.

• Velocity vs. Speed: Newton's First Law specifies constant velocity, which includes both speed and direction. An object moving at a constant speed in a circle is NOT in equilibrium because its direction is changing, implying a non-zero net force.

• The 'Constant Velocity' Keyword: Whenever an exam question mentions 'constant velocity', 'steady speed in a straight line', or 'terminal velocity', immediately conclude that the net force is zero ($\sum F = 0$).

• Don't Forget Friction: In real-world scenarios, objects eventually stop because of the force of friction, not because they 'run out of force'. Always check if friction or air resistance should be included in your force sum.

• Check for Direction Changes: Be careful with objects moving in curves. Even if the speed is constant, a change in direction means the velocity is changing, which requires a net force (centripetal force).

• Sanity Check: If an object is accelerating, the forces in the direction of acceleration MUST be larger than the forces opposing it. If your calculation shows $\sum F = 0$ for an accelerating object, re-evaluate your force identification.