Laws of Motion

The One Thing

Motion changes only when the vector sum of the external forces on an object is non-zero. Newton’s laws quantify this relationship through force, mass, acceleration, momentum, and interactions between bodies.

Reactions, Processes and Experiments

Key Terms

• Force: A push or pull resulting from an interaction; it is a vector quantity measured in newtons (N).
• Inertia: The resistance offered by an object to a change in its state of rest or uniform motion.
• Mass: The measure of an object's inertia and the amount of matter it contains; its SI unit is the kilogram (kg).
• Momentum: The product of mass and velocity, given by p = mv; momentum is a vector quantity.
• Newton's First Law: An object remains at rest or continues in uniform straight-line motion unless acted upon by a net external force.
• Newton's Second Law: The net external force on an object equals the rate of change of its momentum; for constant mass, F_net = ma.
• Newton's Third Law: When one body exerts a force on another, the second body exerts an equal and opposite force on the first.
• Net Force: The vector sum of all external forces acting on an object.
• Equilibrium: A state in which the net force is zero; an object may be at rest or move with constant velocity.
• Free-Body Diagram: A simplified diagram showing an object and all the external forces acting on it.
• Weight: The gravitational force acting on an object, given by W = mg near Earth's surface.
• Normal Reaction: The contact force exerted by a surface perpendicular to the surface.
• Tension: The pulling force transmitted through a taut string, rope, or cable.
• Friction: A contact force that opposes relative motion or the tendency of motion between surfaces.
• Static Friction: Friction that prevents the start of relative motion; its limiting value is f_s(max) = μ_s N.
• Kinetic Friction: Friction acting when surfaces slide over one another; it is given by f_k = μ_k N.
• Coefficient of Friction: A dimensionless ratio that measures the frictional behavior between two surfaces.
• Impulse: The product of force and the time interval for which it acts; impulse equals the change in momentum, J = FΔt = Δp.
• Action-Reaction Pair: Two equal and opposite forces acting on different interacting bodies, as described by Newton's Third Law.

Newton's laws were formulated by Sir Isaac Newton and published in 1687 in his work on mathematical principles of natural philosophy. The SI unit of force is the newton: 1 N = 1 kg m s^-2.

Easily Confused

• Mass and weight: Mass measures inertia and is measured in kilograms; weight is the gravitational force W = mg and is measured in newtons.
• Inertia and mass: Inertia is the resistance to a change in motion; mass is the quantitative measure of that resistance.
• Net force and individual force: Net force is the vector sum of all external forces, not one force selected from the free-body diagram.
• Equilibrium and rest: Equilibrium means zero net force and may involve constant-velocity motion as well as rest.
• Newton’s Third Law pair and balanced forces: An action-reaction pair acts on different bodies and therefore does not cancel on one body; balanced forces act on the same body and can produce zero net force.
• Static and kinetic friction: Static friction prevents the start of relative motion and has limiting value f_s(max) = μ_s N; kinetic friction acts during sliding and is given by f_k = μ_k N.
• Normal reaction and weight: The normal reaction is perpendicular to the surface, whereas weight acts gravitationally downward; N = mg on a horizontal surface only under the stated condition of no vertical acceleration.
• Impulse and force: Impulse depends on both force and time, J = FΔt = Δp; force alone does not specify the change in momentum.
• Contact and non-contact forces: Friction and normal reaction require contact, whereas gravitational and electric forces are non-contact forces.
• Force direction and acceleration direction: Acceleration is in the direction of the net force, not necessarily the direction of an individual force.

What Gets Asked

• State or apply Newton’s First Law: The mark is lost by claiming that an object must be at rest when the net force is zero; it may instead move with constant velocity.
• Calculate acceleration using Newton’s Second Law: Use the net force, not an individual force, and apply a = F_net/m.
• Interpret an action-reaction pair: The forces must be equal and opposite, act on different bodies, and therefore must not be cancelled on a single free-body diagram.
• Construct or interpret a free-body diagram: Include all external forces and assign their directions consistently; omitting a force or using an incorrect direction changes the net force.
• Resolve forces on an inclined plane: The components of weight are mg sin θ parallel to the plane and mg cos θ perpendicular to it; interchanging them costs marks.
• Solve friction problems: Distinguish limiting static friction, f_s(max) = μ_s N, from kinetic friction, f_k = μ_k N, and remember that usually μ_s is greater than μ_k.
• Use momentum and impulse in short-interaction problems: Apply p = mv, J = FΔt = Δp, or J = ∫F dt as appropriate, and use momentum conservation only when the net external force on the isolated system is zero.