Difficulty: Introductory | Prerequisites: Basic algebra, familiarity with speed and direction.
Momentum is one of the first big conservation laws you meet in introductory physics. It ties together mass and velocity into a single quantity that stays constant in any closed system, which is why collisions, crashes and explosions all follow predictable rules. If you are comfortable with what velocity means (speed plus a direction) and can multiply, you have everything you need. This topic sits at the heart of mechanics and feeds directly into energy, impulse and later work on rotational motion.
Momentum equals mass times velocity (p = mv) and it has a direction. In any collision where nothing enters or leaves the system, the total momentum before the collision equals the total momentum after. This holds regardless of the masses, speeds or whether the objects bounce off each other or stick together.
Momentum (p)
The product of an object's mass and its velocity: p = mv. Measured in kilogram-metres per second (kg·m/s). In simple terms, momentum captures how hard it is to stop a moving object.
Velocity (v)
The speed of an object together with its direction of travel, measured in metres per second (m/s). A positive value typically means rightward motion; a negative value means leftward. Think of it as speed with a built-in compass.
Conservation of momentum
In a closed system (no outside forces), the total momentum of all objects before a collision equals the total momentum after. In simple terms, momentum does not appear or disappear during a collision; it just moves between objects.
Air track
A laboratory device that pushes air through small holes in a track so that gliders float on a thin cushion of air, nearly eliminating friction. Think of it as a frictionless surface for studying pure collisions.
Closed system
A system in which no mass enters or leaves and no net external force acts. This is the condition required for conservation of momentum to hold exactly.
The two factors that most affect the outcome of a collision are mass and speed.
A heavier object moving quickly carries far more momentum than a light or slow one.
Example: a bowling ball at 10 m/s knocks down pins; a ping-pong ball at the same speed barely registers.
Momentum is a vector quantity, so direction matters.
Use the sign convention: positive velocity = rightward, negative velocity = leftward.
Example: a 1.5 kg object at 4 m/s has momentum p = 1.5 × 4 = 6 kg·m/s.
To increase an object's momentum, increase its mass, its velocity, or both.
Glider 1 moving left to right at 5.0 m/s has v = +5.0 m/s.
Glider 2 moving right to left at 5.0 m/s has v = −5.0 m/s.
After a head-on collision between equal-mass gliders, each bounces back the way it came, swapping velocities.
Equal mass, different velocities: the gliders exchange velocities on collision.
Equal mass, one stationary: the moving glider stops and the stationary one moves away at the original speed.
Different masses, same speed (opposite directions): the lighter glider rebounds much faster than the heavier one.
Add the individual momenta (with signs) to find total system momentum.
Example: Glider 1, m = 3.0 kg, v = 2.0 m/s, p = 6.0 kg·m/s. Glider 2, m = 2.0 kg, v = −4.0 m/s, p = −8.0 kg·m/s. Total before = −2.0 kg·m/s.
After the collision: Glider 1, v = −2.8 m/s, p = −8.4 kg·m/s. Glider 2, v = 3.2 m/s, p = 6.4 kg·m/s. Total after = −2.0 kg·m/s.
The total momentum before and after the collision is the same, every time, regardless of the mass and velocity combination chosen.
p = mvwhere p is momentum (kg·m/s), m is mass (kg) and v is velocity (m/s).
p_{\text{total, before}} = p_{\text{total, after}}Conservation of momentum: the sum of all momenta before the collision equals the sum after.
m_1 v_1 + m_2 v_2 = m_1 v_1' + m_2 v_2'Expanded form for a two-object collision, where primed values (v') are post-collision velocities.
Car crash safety engineering relies on conservation of momentum to predict how vehicles behave in collisions and to design crumple zones that manage the momentum transfer over a longer time. The same principle explains how a rocket propels itself: exhaust gases carry momentum in one direction, so the rocket gains equal momentum in the opposite direction.
Students often think momentum is always positive. It is not. Momentum is a vector: its sign tells you the direction. A negative momentum simply means the object is moving in the negative direction.
Students sometimes confuse momentum with kinetic energy. They are different quantities. Two objects can have the same momentum but very different kinetic energies because KE depends on v squared.
Students often assume a heavier object always "wins" a collision. Conservation of momentum says the system's total is unchanged, not that the heavier object keeps moving. A heavy object can be brought to rest if the lighter one carries enough speed.
Students sometimes forget to include the sign when adding momenta. Omitting the negative sign will give you the wrong total every time.
Conservation of momentum is one of the most commonly tested principles in introductory physics. Expect to see it on every exam that covers collisions.
You will almost certainly be asked to calculate momentum before and after a collision and show that the totals match.
Pay close attention to sign conventions. Exam questions frequently trip students up by assigning leftward motion a negative velocity.
Be ready to explain in words why total momentum is conserved (closed system, no external forces) as well as to show it with numbers.
True or false: momentum can be negative. (True, because momentum is a vector.)
Fill in the blank: momentum equals ______ times ______. (mass times velocity)
True or false: in a closed system, the total momentum changes during a collision. (False, it stays constant.)
A 2 kg object moves at 3 m/s to the right. Its momentum is ______ kg·m/s. (6)
True or false: if two objects have the same mass and collide head-on with equal speeds, the total momentum of the system is zero. (True)
Q: A 3.0 kg glider moving at 2.0 m/s collides with a 2.0 kg glider moving at −4.0 m/s. What is the total momentum of the system before the collision?
A: p_total = (3.0 × 2.0) + (2.0 × −4.0) = 6.0 + (−8.0) = −2.0 kg·m/s.
Q: After the collision above, Glider 1 has velocity −2.8 m/s and Glider 2 has velocity 3.2 m/s. What is the total momentum after the collision?
A: p_total = (3.0 × −2.8) + (2.0 × 3.2) = −8.4 + 6.4 = −2.0 kg·m/s. The total is unchanged, confirming conservation of momentum.
Q: Two gliders of equal mass collide head-on. Glider 1 is stationary and Glider 2 moves toward it. Describe what happens.
A: The moving glider stops and the stationary glider moves away at the velocity the first glider had. They swap velocities because they have equal mass.
Q: How would you increase the momentum of a single glider on an air track?
A: Increase its mass, increase its velocity, or both. Momentum equals mass times velocity, so raising either factor raises the product.
Q: Explain why the total momentum of a system can be zero even when both objects are moving.
A: If two objects of equal mass move toward each other at equal speeds, their momenta are equal in magnitude but opposite in sign. The positive and negative values cancel, giving a total of zero.
Momentum connects directly to impulse (force multiplied by time), which explains how the same change in momentum can feel gentle or violent depending on how quickly it happens. It also links to kinetic energy and elasticity: while momentum is always conserved in a collision, kinetic energy is only fully conserved in perfectly elastic collisions. Later in the course, these ideas extend to rotational momentum (angular momentum), where the same conservation principle applies to spinning objects.
momentum, conservation of momentum, p = mv, kg·m/s, collision physics, air track, glider collision, elastic collision, closed system, Newton's third law, impulse, change in momentum, vector quantity, momentum before and after, total momentum, mass times velocity