8 Momentum, Change in Momentum & Impulse
Resources
- Video to Watch: Mechanical Universe – Episode 4 – Inertia
- Extra Help: A-Level Physics Tutor
Equations Introduced and Used for this Topic: (All equations can be written and solved as both scalar and vector and all equations are generally solved as vectors)
- Impulse [latex](J) = F t = \Delta p[/latex]
- Change in Momentum [latex](\Delta p) = m \Delta v[/latex]
- Momentum [latex](p) = m v[/latex]
- [latex]\Delta p = p_f - p_i[/latex]
- [latex]\Delta v = v_f - v_i[/latex]
Where…
- [latex]J[/latex] is the impulse or the product of force × time acting on a system, measured in either newton-seconds (Ns) or kilogram-metres per second (kg, m/s)
- [latex]p[/latex] (momentum) is the product of mass times velocity and is measured in either newton-seconds (Ns) or kilogram-metres per second (kg, m/s)
- [latex]\Delta p[/latex] is the change in momentum ([latex]p_f - p_i[/latex] or [latex]m(v_f - v_i)[/latex], measured in either newton-seconds (Ns) or kilogram-metres per second (kg, m/s)
- [latex]m[/latex] is mass, commonly measured in kilograms (kg), grams (g) or tonnes (t)
- [latex]F[/latex] is force, measured in newtons (N)
- [latex]t[/latex] is time, commonly measured in seconds (s) or hours (h)
- [latex]\Delta v[/latex] is the change in an object’s speed generally taken as the difference between the final and initial speed, measured in metres per second (m/s) or kilometres per hour (km/h)
- [latex]v[/latex] is average speed, commonly measured in metres/second (m/s) or kilometres/hour (km/h)
Impulse and momentum are two very important concepts that can be easily derived from Newton’s Second Law and the equation defining acceleration. Specifically using:
[latex]F = m a[/latex] & [latex]a = \dfrac{\Delta v}{t}[/latex]
When you substitute for a in Newton’s Second Law, you are left with:
[latex]F = m \dfrac{\Delta v}{t}[/latex]
Which is more commonly written as:
[latex]F t = m \Delta v[/latex]
Written in this form we now have both the equations for Impulse ([latex]F t[/latex]) and change in momentum ([latex]m \Delta v[/latex]). Both impulse and change in momentum are important physics concepts and have important implications in multiple areas such as analyzing collisions, predicting crash injuries and even helping to analyze rockets and space travel.
If you check out the units used in either F t or in m ∆v, you get two new unit combinations:
Ns and kg m/s (or kg ms-1)
These units are equivalent and can be used for either measure, with the most common unit being Ns because it is quicker to write down. They are interchangeable and you should expect them to be switched around and should require no explanation.
In this chapter we are also adding these two measures of Impulse ([latex]J = F t[/latex]) and Change in Momentum ([latex]\Delta p = m \Delta v[/latex]) to Chapters 1 – 6 (our study of mechanics) and as such will be using all previous equations and variables that have been used up to this point.
8.1 Linea