Linear Momentum
Introduced| English |
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| momentum/məʊˈmentəm/ |
A slow truck and a fast pebble — equally unstoppable
- A truck rolling at walking pace is very hard to stop. So is a small pebble fired from a slingshot.
- One has huge mass, the other huge speed — but both carry a lot of momentum 动量.
- Momentum measures the "quantity of motion" packed into a moving object.
- It is the idea that makes collisions and recoil predictable.
Momentum is mass times velocity
- Momentum is $\vec p = m\vec v$ — mass multiplied by velocity.
- It is a vector: it points the same way the object moves.
- Its units are $\text{kg}\cdot\tfrac{\text{m}}{\text{s}}$ (there is no special name).
- Double the mass or double the speed, and you double the momentum.
Compare two momenta
Change each mass and speed and read off the momentum p = mv of each object.
What is the momentum of a $1500\ \text{kg}$ car moving at $20\ \tfrac{\text{m}}{\text{s}}$, in $\text{kg}\cdot\tfrac{\text{m}}{\text{s}}$?
$p = mv = 1500 \times 20 = 30\,000\ \text{kg}\cdot\tfrac{\text{m}}{\text{s}}$.
Momentum equals mass times ____.
$\vec p = m\vec v$ — mass times velocity.
If you double an object's speed without changing its mass, its momentum:
Momentum is linear in speed ($p = mv$), so doubling $v$ doubles $p$ — unlike kinetic energy, which quadruples.
Why momentum is useful
- The larger an object's momentum, the harder it is to stop or turn.
- A big truck and a fast bullet can need the same effort to halt.
- Momentum, unlike kinetic energy, depends on speed to the first power, not the square.
- That makes it the natural bookkeeping quantity for impacts.
Select all true statements about momentum.
Momentum $= mv$ is a vector, linear (not squared) in speed, so mass and speed can trade off.
Direction counts
- Because momentum is a vector, its sign matters in one dimension.
- Two objects with the same speed but opposite directions have opposite momenta.
- When you add momenta, add them as vectors — they can partly cancel.
- A system's total momentum is the vector sum of every object's $m\vec v$.
Momentum is a vector, so its direction matters.
$\vec p = m\vec v$ points along the velocity; opposite directions give opposite signs.
Two identical $2\ \text{kg}$ balls move at $3\ \tfrac{\text{m}}{\text{s}}$ in opposite directions. What is the total momentum, in $\text{kg}\cdot\tfrac{\text{m}}{\text{s}}$?
$+6$ and $-6$ cancel: total momentum $= 0$. The vectors sum to zero.
Momentum is a vector, so direction cannot be ignored. Two identical balls moving at the same speed in opposite directions have a total momentum of zero, even though each one clearly has momentum. Always keep track of signs.
Find the momentum of a $1500\ \text{kg}$ car moving at $20\ \tfrac{\text{m}}{\text{s}}$.
- $p = mv = 1500 \times 20 = 30\,000\ \text{kg}\cdot\tfrac{\text{m}}{\text{s}}$, in the direction of motion.
A $0.02\ \text{kg}$ bullet would need a speed of $1.5$ million $\tfrac{\text{m}}{\text{s}}$ to match it — which is why the car is "unstoppable" by comparison.
Momentum is the quantity of motion, $\vec p = m\vec v$ (a vector, in $\text{kg}\cdot\tfrac{\text{m}}{\text{s}}$). A large mass or a large speed gives large momentum, so a slow truck and a fast pebble can match. Because it is a vector, direction and sign matter.