Impulse-Momentum Theorem formula |
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| \( J \;=\; \Delta p \) | ||
| Symbol | English | Metric |
| \( J \) = Impulse | \(lbf \;/\; sec\) | \(N \;/\; s\) |
| \( \Delta p \) = Change in Momentum | \(lbm-ft\;/\;sec\) | \(kg-m\;/\;s\) |
Impulse-Momentum theorem, abbreviated as \(J\), is a basic principle in Newtonian mechanics that establishes a direct relationship between the impulse delivered to an object and the resulting change in its momentum. It states that the impulse acting on an object is equal to the change in the object's linear momentum.
Impulse-Momentum Theorem formula
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\( F \cdot \Delta t \;=\; m \cdot \Delta v \) (Impulse-Momentum) \( F \;=\; \dfrac{ m \cdot \Delta v }{ \Delta t }\) \( m \;=\; \dfrac{ F \cdot \Delta t }{ \Delta v }\) \( \Delta v \;=\; \dfrac{ F \cdot \Delta t }{ m }\) \( \Delta t \;=\; \dfrac{ m \cdot \Delta v }{ F }\) |
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| Symbol | English | Metric |
| \( F \) = Force | \(lbf\) | \(N\) |
| \( m \) = Object Mass | \(lbm\) | \(kg\) |
| \( \Delta v \) = Change in Velocity | \(ft\;/\;sec\) | \(m\;/\;s\) |
| \( \Delta t \) = Change in Time | \(sec\) | \(s\) |
The theorem tells us that to change an object’s momentum (to speed it up, slow it down, or change its direction), a net force must act on it for some duration of time, and the product of that force and time determines exactly how much the momentum changes. This is why the same change in momentum can be achieved either by applying a large force for a short time (e.g., a bat hitting a baseball) or a smaller force for a longer time (e.g., air resistance gradually slowing a falling feather). The theorem is derived directly from Newton’s second law by integrating both sides over time, making it especially useful for analyzing collisions, explosions, rocket propulsion, and any situation where forces act over brief or varying time intervals rather than constant acceleration over distance.
