Linear momentum
Newton's Laws & Momentum - OCR A-Level Physics
Key Definition
Linear momentum
The product of an object's mass and its velocityThe rate of change of displacement. A vector quantity. Measured in $\text{m s}^{-1}$.. A vectorA quantity with both magnitude and direction (e.g. force, velocity, displacement). quantity, pointing in the same direction as the velocity. SI unit: $\text{kg m s}^{-1}$, equivalent to N s.
The product of an object's mass and its velocityThe rate of change of displacement. A vector quantity. Measured in $\text{m s}^{-1}$.. A vectorA quantity with both magnitude and direction (e.g. force, velocity, displacement). quantity, pointing in the same direction as the velocity. SI unit: $\text{kg m s}^{-1}$, equivalent to N s.
$$p = mv$$
- Momentum is a vector: direction matters. Always choose and state a positive direction before doing calculations. Objects moving in the negative direction have negative momentum.
- A heavy, slow object can carry the same momentum as a light, fast object. A 1500 kg car at 2.0 $\text{m s}^{-1}$ has the same 3000 $\text{kg m s}^{-1}$ as a 0.060 kg tennis ball at 50000 $\text{m s}^{-1}$ (clearly unphysical for the ball, but illustrates the point).
- Worked example: a 0.045 kg golf ball leaves the tee at 75 $\text{m s}^{-1}$. $p = (0.045)(75) = 3.4 \; \text{kg m s}^{-1}$.
- The total momentum of a system is the vector sum of individual momenta: $p_{\text{total}} = \Sigma m_i v_i$ (with signs).
- The unit $\text{kg m s}^{-1}$ is identical to N s. This equivalence is essential when working with impulse: $F \Delta t = \Delta p$ has consistent units on both sides.
Common Mistake
MEDIUM
Wrong: Treating momentum as a scalar and adding magnitudes when objects move in opposite directions.
Right: Momentum is a vector. If a 2.0 kg trolley moves right at 3.0 $\text{m s}^{-1}$ and a 1.0 kg trolley moves left at 4.0 $\text{m s}^{-1}$, take right as positive: $p_{\text{total}} = (2.0)(3.0) + (1.0)(-4.0) = +2.0 \; \text{kg m s}^{-1}$. The system has net momentum to the right, not 10 $\text{kg m s}^{-1}$.
Right: Momentum is a vector. If a 2.0 kg trolley moves right at 3.0 $\text{m s}^{-1}$ and a 1.0 kg trolley moves left at 4.0 $\text{m s}^{-1}$, take right as positive: $p_{\text{total}} = (2.0)(3.0) + (1.0)(-4.0) = +2.0 \; \text{kg m s}^{-1}$. The system has net momentum to the right, not 10 $\text{kg m s}^{-1}$.
Examiner Tips and Tricks
- Quote units as $\text{kg m s}^{-1}$ or N s. Both score. Plain "kg m/s" is also accepted.
- When asked to define momentum, write "the product of mass and velocity" AND state that it is a vector. Both points are needed for full marks.