Impulse-momentum theorem states that the impulse of force on a body is equal to the change in momentum of force on a body is equal to the change in momentum of the body.
i.e., \(\vec{J}=\vec{F}t=\vec{p}_2-\vec{p}_1\)
Proof. According to Newton’s Second law of motion, we know that
\(\vec{F}\) = \(\frac{d\vec{p}}{dt}\)
or \(\vec{F}dt = d\vec{p}\)
When \(\vec{F}\) = constant force acting on the body.
Suppose \(\vec{p}_1\) and \(\vec{p}_2\) be the linear moments of the body at time t = 0 and t respectively.
∴ Integrating equation (i) within these limits, we get
\(∫^t_0\vec{F}dt=∫^{\vec{p}_2}_{\vec{p}_1}d\vec{p}\)
⇒ \(\vec{F}∫^t_0dt=∫^{\vec{p}_2}_{\vec{p}_1}d\vec{p}\)
\(\vec{F}[t]^t_0=[p]^{p_2}_{p_1}\)
\(\vec{F}t=\vec{p}_2-\vec{p}_1\)
\(\vec{J}=\vec{p}_2-\vec{p}_1\)
