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Momentum and Impulse Relationship 📂Physics

Momentum and Impulse Relationship

Definition

  • Momentum

    The product of an object’s mass and velocity is called momentum, denoted by pp. While in high school physics, velocity vv is often used to represent the state of motion of an object, in college physics, momentum pp is more commonly used.

    p⃗=mv⃗[kg⋅m/s] \vec{p}=m\vec{v}[kg\cdot m/s]

    Since velocity vv is a vector, so is momentum. Since mass mm is always positive, the direction of velocity and momentum are always the same. It is evident that the larger the mass or the magnitude of velocity, the larger the momentum. If represented on a graph, it would look like the figure below. In the case of constant acceleration linear motion, it is simply the multiplication of mass mm, hence the shape of the graph is the same.

    2.jpg

  • Impulse

    The product of the force exerted on an object and the duration is called impulse, denoted by II.

    I⃗=F⃗⋅Δt[N⋅s] \vec{I}=\vec{F}\cdot \Delta t[N\cdot s]

    Since force F⃗\vec{F} is a vector, impulse is also a vector. Since time tt is always positive, the direction of the force and the impulse are the same. It is understood that the larger the magnitude of the force, or the longer the force acts, the greater the impulse. This can be represented in a graph as shown below.

    1.jpg

Formulas

Relationship between Momentum and Impulse

F⃗=\ma=mΔv⃗Δt=mΔv⃗Δt=Δp⃗ΔtI⃗= F⃗⋅Δt \begin{align} \vec{F} =&\ma=m\frac { \Delta \vec{v} }{ \Delta t }=\frac { m\Delta \vec{v} }{ \Delta t }=\frac { \Delta \vec{p} }{ \Delta t } \\ \vec{I}=&\ \vec{F}\cdot \Delta t \end{align}

From equation 1 and equation 2, the following can be derived:

I⃗=F⃗⋅Δt=Δp⃗ \vec{I}=\vec{F}\cdot \Delta t=\Delta \vec{p}

As can be seen from the equation, ‘impulse equals the change in momentum’. It is also evident that force F⃗\vec{F} is the rate of change of momentum over time.