Change in momentum

1. Understanding Change in Momentum

• An object's momentum changes when its velocity changes in either magnitude (size) or direction.
• Momentum remains constant in a collision (if the object does not break apart or reach extreme speeds).
• The change in velocity causes the change in momentum.

2. Formulas for Change in Momentum

Change in Velocity

$\Delta v = v_f - v_i$

where:

• $\Delta v =$ change in velocity $(m/s)$
• $v_f =$ final velocity $(m/s)$
• $v_i =$ initial velocity $(m/s)$

Change in Momentum

$\Delta p = p_f - p_i$

$\Delta p = mv_f - mv_i$

$\Delta p = m(v_f - v_i)$

where:

• $\Delta p$ $=$ change in momentum $(kg·m/s)$
• $p_f =$ final momentum $(kg·m/s)$
• $p_i =$ initial momentum $(kg·m/s)$
• $m =$ mass $(kg)$

3. Steps to Solve Momentum Problems

1. Draw a sketch of the situation.
2. Choose a positive direction (e.g. right is positive).
3. Write down the given values using symbols.
4. Include correct signs for initial and final velocity.
5. Select the correct formula from the information sheet.
6. Substitute values and solve.

5. Key Takeaways

• Momentum changes when velocity changes.

• Change in momentum is calculated as . $\Delta p = mv_f - mv_i$

• Always assign direction when working with momentum.