Momentum formulas drop them down

Linear momentum ($\vec{p}$) is the product of an object's mass ($m$) and its velocity ($\vec{v}$). It is a vector quantity.

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

The unit for momentum is $\text{kg} \cdot \text{m/s}$.

Impulse ($\vec{J}$) is the change in momentum of an object. It is also equal to the product of the net force ($\vec{F}_{net}$) acting on an object and the time interval ($\Delta t$) over which the force acts.

$$\boxed{\vec{J} = \Delta \vec{p} = \vec{p}_f - \vec{p}_i = m\vec{v}_f - m\vec{v}_i = \vec{F}_{net}\Delta t}$$

The unit for impulse is $\text{N} \cdot \text{s}$ or $\text{kg} \cdot \text{m/s}$.

For a closed system (where no external forces act), the total linear momentum before a collision or interaction is equal to the total linear momentum after the collision or interaction. For two objects:

$$\boxed{m_1\vec{v}_{1i} + m_2\vec{v}_{2i} = m_1\vec{v}_{1f} + m_2\vec{v}_{2f}}$$

where:

• $m_1, m_2$ are the masses of the two objects.
• $\vec{v}_{1i}, \vec{v}_{2i}$ are their initial velocities (before collision).
• $\vec{v}_{1f}, \vec{v}_{2f}$ are their final velocities (after collision).