Momentum
Introduced| English | Meaning |
|---|---|
| momentum/məʊˈmentəm/ | The product of mass and velocity. |
| conservation of momentum/ˌkɒnsəˈveɪʃn ɒv məʊˈmentəm/ | Total momentum remains constant when no resultant external force acts. |
| collision/kəˈlɪʒn/ | An interaction in which objects or particles strike or exert large forces on one another over a short time. |
| explosion/ekˈspləʊʒn/ | A rapid release of stored energy that can cause an object or system to separate into parts moving apart. |
| conserved/kənˈsɜːvd/ | Remaining constant in total within an isolated system or under the specified conditions. |
| elastic/ɪˈlæstɪk/ | Describing a material or object that returns to its original shape or size after a deforming force is removed, within its elastic limit. |
| kinetic energy/kɪˈnetɪk ˈenədʒi/ | The energy an object has because of its motion. |
| inelastic/ɪnɪˈlæstɪk/ | Describing a deformation that is not fully recovered on unloading, or a collision in which total kinetic energy is not conserved. |
The crash that proves physics works
- When two cars collide, the total momentum 动量 before equals the total momentum after — even though the cars are crumpled and stopped.
- Conservation of momentum 动量守恒 is one of the most powerful laws in physics. It works for billiard balls, rockets, and subatomic particles.
What is momentum?
- Momentum = mass × velocity (a vector): $\mathbf{p} = m\mathbf{v}$.
- Units: $\text{kg m s}^{-1}$ (or equivalently, N s).
- Because it's a vector, direction matters: a 2 kg ball going right at 3 m/s has momentum $+6$; going left, $-6$.
Worked example. A 0.5 kg tennis ball hits a wall at $20\text{ m s}^{-1}$ and bounces back at $15\text{ m s}^{-1}$. Change in momentum $= 0.5(15) - 0.5(-20) = 7.5 + 10 = 17.5\text{ kg m s}^{-1}$.
A Newton's cradle demonstrates conservation of momentum
Conservation of momentum
m₁u₁ + m₂u₂ = (m₁+m₂)v
Two trolleys collide and stick together — the total momentum before equals the total after.
Momentum is defined as:
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Momentum = mass × velocity, a vector quantity.
A 0.5 kg ball hits a wall at 20 m/s and bounces back at 15 m/s. Change in momentum (kg m/s)?
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Change = 0.5(15) − 0.5(−20) = 7.5 + 10 = 17.5 kg m/s.
Conservation of momentum
- In a collision 碰撞 (or explosion 爆炸), total momentum is conserved 守恒:
Watch the signs. Momentum is a vector. If one object moves left and another right, one velocity is positive and the other negative. Getting the signs wrong is the most common error.
Total momentum before equals total momentum after a collision
In a collision, the total momentum of the two bodies is conserved.
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Total momentum before equals total momentum after the collision.
When two objects move in opposite directions, their momenta have opposite signs.
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Momentum is a vector — opposite directions mean opposite signs.
Worked example — collision
- A 2 kg body at $3\text{ m s}^{-1}$ hits a stationary 1 kg body and they stick together.
Total momentum before equals total momentum after: 2(3) + 1(0) = (2+1)v.
- Before: $2(3) + 1(0) = 6\text{ kg m s}^{-1}$.
- After: $(2+1)v = 3v$.
- Conservation: $3v = 6 \Rightarrow v = 2\text{ m s}^{-1}$.
A 2 kg body moving at 3 m/s hits a stationary 1 kg body and they stick together. What is their common speed (m/s)?
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2(3) + 1(0) = (2+1)v, so 6 = 3v, giving v = 2 m/s.
Types of collision
- Perfectly elastic 弹性: kinetic energy 动能 is conserved (rare in practice).
- Inelastic 非弹性: kinetic energy is lost (most real collisions).
- Perfectly inelastic: the bodies stick together (maximum energy loss).
- Momentum is conserved in all types — only kinetic energy may change.
- In a collision the total linear momentum is unchanged — the conservation of linear momentum.
In a perfectly elastic collision, which quantity is conserved (in addition to momentum)?
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In a perfectly elastic collision, both momentum and kinetic energy are conserved.
You've got it
- momentum = mass × velocity (a vector)
- conservation: $m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2$
- total momentum is the same before and after a collision
- momentum is conserved in all collisions; kinetic energy only in elastic ones
Write from a common speed of 4 metres per second
- A 2 kg body at 6 metres per second sticks to a stationary 1 kg body.
- Find the common speed.
A 2 kg body moving at 6 metres per second sticks to a stationary 1 kg body. What is their common speed?
2 times 6 is 12, and 12 divided by 3 is 4.
What is the common speed?
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12 divided by 3 is 4 metres per second. Other options — 17.5 (the lesson momentum change of a bounce); 6 metres per second (the original speed).