Cambridge Syllabus Notes

Momentum and Newton’s Laws of Motion

Objective

State and apply each of Newton’s laws of motion to solve problems and answer exam questions.

Newton’s First Law (Law of Inertia) ⚖️

Statement: An object at rest stays at rest, and an object in motion continues in a straight line at constant speed unless acted upon by an external force.

Analogy: Think of a soccer ball on a field – it won’t move until someone kicks it. Once kicked, it keeps rolling until friction or a goal post stops it.

Example: A 2 kg crate on a frictionless table remains stationary until a worker pushes it. The worker’s push is the external force that changes its state.

Exam tip: Look for phrases like “no net external force” or “constant velocity” to identify situations governed by the first law.

Newton’s Second Law (Law of Acceleration) 🚀

Statement: The net external force acting on an object is equal to the mass of the object multiplied by its acceleration: $$F_{\text{net}} = ma$$

Analogy: Pushing a shopping cart: the harder you push (larger force), the faster it accelerates. If the cart is heavier, you need a larger force to achieve the same acceleration.

Example: A 5 kg sled is pulled with a 20 N horizontal force. Its acceleration is $$a = \frac{F}{m} = \frac{20}{5} = 4\ \text{m/s}^2.$$

Exam tip: Always check the direction of the force and acceleration. Use a sign convention (positive to the right, negative to the left) to avoid mistakes.

Newton’s Third Law (Action–Reaction) 🧲

Statement: For every action force, there is an equal and opposite reaction force.

Analogy: When you jump off a small boat, you push the boat backward while the boat pushes you forward with an equal force.

Example: A rocket expels exhaust gases at 3000 m/s. The rocket experiences an upward thrust equal in magnitude to the downward force on the gases.

Exam tip: Remember that the action–reaction pair acts on different objects. Don’t add them together when solving for a single object’s motion.

Momentum (p) 📐

Definition: Momentum is the product of an object’s mass and velocity: $$p = mv$$

Conservation: In an isolated system with no external forces, total momentum remains constant.

Example: Two ice skaters (each 60 kg) push off each other. If one moves at 2 m/s to the right, the other moves at 1.33 m/s to the left to conserve momentum.

Object	Mass (kg)	Velocity (m/s)	Momentum (kg·m/s)
Skater A	60	2	120
Skater B	60	-1.33	-80
Total			40

Applying Newton’s Laws in Practice

Identify all forces acting on the object (magnitude, direction).
Choose a coordinate system and assign signs to directions.
Apply the second law: $$F_{\text{net}} = ma$$ to find acceleration.
Use kinematic equations to find velocity or displacement if needed.
Check consistency with the first and third laws (e.g., no net force implies constant velocity).

Exam tip: When a problem involves multiple objects, set up equations for each using the third law to relate forces. Then solve simultaneously for unknowns.

state and apply each of Newton’s laws of motion