Forces and Momentum 🚗💥

students, in everyday life, motion is full of pushes, pulls, collisions, and changes in speed. A soccer ball slows down after a kick, a car stops when brakes are applied, and a shopping trolley becomes harder to stop when it is loaded with groceries. All of these situations are explained by forces and momentum. In this lesson, you will learn the main ideas, important terms, and core IB Physics SL reasoning used to describe how forces change motion and how momentum is conserved in interactions.

What you will learn

• How to define force, momentum, impulse, and net force
• How Newton’s laws connect force to changes in motion
• How momentum is calculated and why it matters in collisions
• How impulse relates force, time, and change in momentum
• How these ideas fit into the wider topic of Space, Time and Motion

By the end, you should be able to explain real-world examples and solve standard IB Physics SL problems using clear physics reasoning.

Forces: the cause of change in motion

A force is a push or pull that can change an object’s motion or shape. In physics, the key idea is that forces do not simply “make things move.” Instead, they cause acceleration, which means a change in velocity. Velocity includes both speed and direction.

The unit of force is the newton, written as $\text{N}$. One newton is the force needed to give a mass of $1\,\text{kg}$ an acceleration of $1\,\text{m s}^{-2}$, so $1\,\text{N} = 1\,\text{kg m s}^{-2}$.

A very important idea in mechanics is the net force, also called the resultant force. This is the overall force acting on an object after all forces are combined. If the net force is zero, the object is in equilibrium. It may be at rest or moving at constant velocity. If the net force is not zero, the object accelerates.

For example, students, imagine pushing a box across a floor. Your push is one force, friction is another force, and the weight of the box acts downward while the floor pushes upward with a normal force. If your push is greater than friction, the box speeds up. If friction is greater, it slows down. If the forces balance, it moves at constant velocity or stays still.

Newton’s laws and why motion changes

The IB syllabus expects you to understand the relationship between forces and motion using Newton’s laws.

Newton’s first law

An object remains at rest or continues in uniform motion in a straight line unless acted on by a net external force. This law shows that force is not needed to maintain motion, only to change motion.

Think about a puck gliding on ice. Once it is moving, it can keep moving for a long time because friction is small. In real life, friction and air resistance usually stop objects from moving forever, so a net force is almost always present.

Newton’s second law

The acceleration of an object is proportional to the net force and inversely proportional to its mass:

$$\vec{F}_{\text{net}} = m\vec{a}$$

This equation is central to Force and Momentum. It tells us that larger net forces produce larger accelerations, but heavier objects accelerate less for the same force.

For example, if a small trolley and a large trolley are pushed with the same force, the smaller trolley accelerates more because its mass is smaller. This is why loaded vehicles need more force to speed up or stop.

Newton’s third law

If object A exerts a force on object B, then object B exerts an equal and opposite force on object A. These forces act on different objects, so they do not cancel each other.

A good example is walking. Your foot pushes backward on the ground, and the ground pushes forward on you. That forward force helps you move. Another example is a rocket: exhaust gases are pushed backward, and the rocket is pushed forward.

Momentum: “motion quantity”

Momentum describes how difficult it is to stop a moving object. It depends on both mass and velocity. The momentum of an object is

$$\vec{p} = m\vec{v}$$

where $\vec{p}$ is momentum, $m$ is mass, and $\vec{v}$ is velocity.

Momentum is a vector, which means direction matters. If a car moves east, its momentum points east. If it reverses, its momentum changes direction.

This explains why large and fast objects are harder to stop. A truck with mass $m$ moving at speed $v$ usually has much greater momentum than a cyclist, so it requires a much bigger force or longer time to stop safely.

The SI unit of momentum is $\text{kg m s}^{-1}$. Since $\vec{p} = m\vec{v}$, you can also think of momentum as “mass in motion.”

In many IB problems, you may be asked to compare momenta. For instance, if two objects have the same mass but one moves twice as fast, the faster one has twice the momentum. If one object has twice the mass and the same speed, it also has twice the momentum.

Impulse: force acting over time ⏱️

A force does not only have a size; it also acts for a certain time. The product of force and time is called impulse.

$$\vec{J} = \vec{F}\Delta t$$

Impulse is equal to the change in momentum:

$$\vec{J} = \Delta \vec{p}$$

So we can write

$$\vec{F}\Delta t = \Delta \vec{p}$$

This relationship is extremely useful. It means the same change in momentum can be produced by a large force for a short time or a smaller force for a longer time.

A real-life example is a car airbag. During a crash, the passenger’s momentum must drop to zero. The airbag increases the time over which this change happens, which reduces the average force on the passenger. This is why airbags and crumple zones improve safety.

Another example is catching a ball. If students catches a ball by moving your hands backward as you catch it, you increase the stopping time. The force on your hands becomes smaller, making the catch less painful.

Conservation of momentum in collisions

A major idea in this topic is that in a closed system with no external net force, total momentum is conserved. That means the total momentum before an interaction equals the total momentum after the interaction.

$$\vec{p}_{\text{before}} = \vec{p}_{\text{after}}$$

For two objects moving in one dimension, this can be written as

$$m_1\vec{u}_1 + m_2\vec{u}_2 = m_1\vec{v}_1 + m_2\vec{v}_2$$

where $\vec{u}$ represents initial velocity and $\vec{v}$ represents final velocity.

This conservation law applies to collisions, explosions, and separations. It is one of the most powerful tools in mechanics.

Example: collision on a track

Imagine a moving trolley collides with a stationary trolley and they stick together. Before the collision, only the first trolley has momentum. After the collision, both move together with a common velocity. Because momentum is conserved, the final speed is usually smaller than the original speed of the first trolley.

This type of collision is called a perfectly inelastic collision because the objects stick together. Momentum is conserved, but kinetic energy is not fully conserved. Some kinetic energy is transformed into sound, heat, and deformation.

Example: explosion

If a cart at rest breaks into two pieces, the total momentum before the explosion is zero. Afterward, the pieces move in opposite directions with equal and opposite momenta, so total momentum remains zero.

This is why fireworks and recoil examples work. If a gun fires a bullet forward, the gun recoils backward. The total momentum of the system stays constant if external forces are negligible.

Forces, momentum, and energy in the bigger picture

Force and momentum are closely connected to the rest of Space, Time and Motion because they explain how motion changes over time.

• Forces explain why velocity changes.
• Momentum describes the motion of an object in a compact way.
• Impulse connects force to time and momentum change.
• Energy helps explain where motion goes during interactions.

In many real situations, both momentum and energy ideas are needed. For example, in a car crash, momentum conservation helps predict the motion after impact, while energy ideas help explain deformation and heating. In sports, a bat transferring momentum to a ball also changes the ball’s kinetic energy.

When solving IB Physics SL questions, always identify the system, list the known quantities, and decide whether momentum is conserved. If external forces are negligible during a short collision, conservation of momentum is usually the right method. If a force acts over time, impulse may be the easier route.

Conclusion

Forces and momentum are core ideas in physics because they explain how and why motion changes. Forces cause acceleration, momentum measures motion and direction, and impulse links force with time and momentum change. In collisions and explosions, total momentum is conserved when external net force is negligible. These ideas are not only important for exams, students, but also for understanding everyday events like braking, catching, crashes, and sports. Together, they form a foundation for the wider study of Space, Time and Motion.

Study Notes

• A force is a push or pull that can change motion or shape.
• The net force determines whether an object accelerates.
• Newton’s second law is $\vec{F}_{\text{net}} = m\vec{a}$.
• Momentum is calculated using $\vec{p} = m\vec{v}$.
• Momentum is a vector, so direction matters.
• Impulse is $\vec{J} = \vec{F}\Delta t$ and equals $\Delta \vec{p}$.
• Increasing stopping time reduces average force in a crash.
• In a closed system, total momentum is conserved: $\vec{p}_{\text{before}} = \vec{p}_{\text{after}}$.
• Inelastic collisions conserve momentum but not kinetic energy.
• Forces and momentum are key tools for understanding motion, collisions, and safety in the real world 🚦