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183_notes:acceleration [2014/07/10 20:49] – [Acceleration] caballero | 183_notes:acceleration [2014/07/22 19:58] – pwirving | ||
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===== Acceleration & The Change in Momentum ===== | ===== Acceleration & The Change in Momentum ===== | ||
- | As you read, the motion of a system is governed by the Momentum Principle (aka " | + | As you read, [[183_notes: |
==== Newton' | ==== Newton' | ||
- | The Momentum Principle (or Newton' | + | The Momentum Principle (or Newton' |
$$\vec{F}_{net} = m\:\vec{a} = \dfrac{\Delta\vec{p}}{\Delta t}$$ | $$\vec{F}_{net} = m\:\vec{a} = \dfrac{\Delta\vec{p}}{\Delta t}$$ | ||
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$$\vec{a}_{avg} = \dfrac{\Delta \vec{v}}{\Delta t} = \dfrac{\vec{v}_f - \vec{v}_i}{\Delta t}$$ | $$\vec{a}_{avg} = \dfrac{\Delta \vec{v}}{\Delta t} = \dfrac{\vec{v}_f - \vec{v}_i}{\Delta t}$$ | ||
- | If we allow the time interval to shrink (as we did with the average velocity), we obtain the instantaneous acceleration, | + | If we allow the time interval to shrink ([[: |
$$\vec{a} = \lim_{\Delta t \rightarrow 0}\vec{a}_{avg} = \lim_{\Delta t \rightarrow 0}\dfrac{\Delta \vec{v}}{\Delta t} = \dfrac{d\vec{v}}{dt}$$ | $$\vec{a} = \lim_{\Delta t \rightarrow 0}\vec{a}_{avg} = \lim_{\Delta t \rightarrow 0}\dfrac{\Delta \vec{v}}{\Delta t} = \dfrac{d\vec{v}}{dt}$$ | ||
- | The units of acceleration are meters per second per second ($\dfrac{m}{s^2}$. | + | The units of acceleration are meters per second per second ($\dfrac{m}{s^2}$). |
+ | ==== Why not just use change in momentum? ==== | ||
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+ | If you have one way of describing motion (i.e., using the concept of a change in momentum), why should you learn about acceleration? | ||
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+ | Acceleration is a useful concept in mechanics, because it can help characterize the motion of systems (e.g., constant velocity motion has no acceleration). | ||
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+ | While you can obtain this information by determining the forces acting on the system, it's possible to use observational information (how the position changes) to determine how the system is accelerating without knowing the system' | ||