2.4 Newton's First Law

Newton's first law says a system keeps the same velocity, including staying at rest, when the net force on it is zero. That zero net force condition is called translational equilibrium, written as the vector sum of all forces equaling zero. In AP Physics 1, this topic connects free-body diagrams, balanced forces, inertial frames, and constant-velocity motion.

Newton's first law is the starting point for any problem where an object moves at constant velocity or sits still, and the exam expects you to explain that motion in words before you plug in numbers.

Zero Net Force Means Constant Velocity

• Net force is the vector sum of every force on a system, so direction matters as much as magnitude.
• Translational equilibrium means the net force is zero, written $\sum_{i} \vec{F}_{i} = 0$.
• Zero net force means constant velocity, which includes staying at rest (no acceleration).
• Forces can balance in one direction and not in another; velocity only changes along the unbalanced direction.
• An inertial reference frame is one where Newton's first law holds, meaning a non-accelerating frame.
• Constant velocity does not require zero force, only zero net force.

Net Force Formula

The net force formula is the vector sum of all forces on a system:

$\vec{F}_{\text{net}} = \sum_i \vec{F}_i$

For Newton's first law, the key condition is $\vec{F}_{\text{net}} = 0$. That means the forces are balanced and the system's velocity stays constant. If the x-direction forces balance but the y-direction forces do not, only the y-component of velocity changes, so always check each axis separately.

Core Concepts

Vector sum of forces

The net force on a system is found by adding all forces as vectors, accounting for both magnitude and direction.

• Forces in the same direction add together; forces in opposite directions subtract.
• If forces act at angles, break them into components first, then add the components.

Translational equilibrium

Translational equilibrium happens when the vector sum of all forces on a system equals zero, so there is no acceleration.

• Mathematically: $\sum_{i} \vec{F}_{i} = 0$
  • $\sum$ means the sum of all forces ($\vec{F}_{i}$) on the system
  • the subscript $i$ labels each individual force
• A system in equilibrium can be at rest (often called static equilibrium) or moving at constant velocity (often called dynamic equilibrium).
• Example: A book resting on a table has gravity pulling down and the normal force pushing up. These balance, so the book stays at rest.

Newton's first law

Newton's first law, also called the law of inertia, states that a system keeps a constant velocity unless an unbalanced force acts on it.

• If the net force is zero, the velocity stays constant, whether that velocity is zero or some steady value.
• Example: A hockey puck gliding on nearly frictionless ice feels close to zero net force, so it keeps moving at roughly constant velocity.

Balanced vs unbalanced forces

• Balanced forces sum to zero and keep velocity constant.
• Unbalanced forces produce a nonzero net force and cause acceleration in the direction of that net force.
• Forces can be balanced in one dimension and unbalanced in another. Only the velocity component along the unbalanced direction changes; the component along a balanced direction stays constant.
• Example: A box sliding across a floor can have balanced vertical forces (normal force up, gravity down) while a horizontal push or friction is unbalanced. The box accelerates horizontally but its vertical velocity stays constant.

Inertial reference frame

An inertial reference frame is one where Newton's first law holds, so an observer in that frame can describe motion correctly using Newton's laws.

• Non-accelerating frames, like a stationary lab bench or a car moving at constant velocity, are inertial.
• Accelerating frames, like an elevator speeding up or a car turning a corner, are non-inertial, and Newton's first law does not appear to hold there without extra analysis.
• Earth's surface works as an approximately inertial frame for most everyday problems.

Using Balanced Forces to Explain Constant Velocity

Problem Solving:

• Start by drawing a free-body diagram with each force as an arrow from a single dot.
• Pick axes so one axis lines up with the motion or the obvious force directions.
• Write the equilibrium condition for each axis separately: $\sum F_x = 0$ and $\sum F_y = 0$ when velocity is constant in that direction.
• Solve for the unknown force using the balanced-force equations.

Free Response:

• When a question asks you to explain why an object moves at constant velocity, state that the net force is zero and the forces are balanced.
• Connect your words to your diagram and equations. The qualitative-quantitative translation question rewards moving cleanly between a verbal claim, a free-body diagram, and the equation $\sum_{i} \vec{F}_{i} = 0$.
• Be precise: say "constant velocity" or "zero acceleration," not just "no force," since forces can be present but balanced.

Common Trap:

• Watch for setups where forces balance vertically but not horizontally (or the reverse). Treat each direction on its own so you do not miss an acceleration in one axis.

Common Misconceptions

• Misconception: Constant velocity means no forces act.
  Actually: Constant velocity does not mean no forces act. It means the forces add to zero, so the net force is zero.
• Misconception: An object at rest is force free.
  Actually: An object at rest is not "force free." It is usually in equilibrium with several balanced forces, like weight and normal force.
• Misconception: Newton's first law is only about objects at rest.
  Actually: Newton's first law is not only about objects at rest. Constant-velocity motion in a straight line also counts as zero net force.
• Misconception: Balanced forces in one direction guarantee balanced forces everywhere.
  Actually: Balanced forces in one direction do not guarantee balanced forces everywhere. Check each axis separately.
• Misconception: Newton's first law fails because of the object in a non-inertial frame.
  Actually: A non-inertial frame, like an accelerating elevator, is not where Newton's first law fails because of the object; it appears to fail because the frame itself is accelerating.

Related AP Physics 1 Guides

• 2.1 Systems and Center of Mass
• 2.2 Forces and Free-Body Diagrams
• 2.3 Newton's Third Law
• 2.5 Newton's Second Law
• 2.6 Gravitational Force
• 2.7 Kinetic and Static Friction