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183_notes:acceleration [2014/07/10 20:25] – created caballero | 183_notes:acceleration [2014/07/10 20:54] – [Acceleration] caballero | ||
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- | ===== Acceleration & the Change in Momentum ===== | + | ===== Acceleration & The Change in Momentum ===== |
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+ | As you read, [[183_notes: | ||
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+ | ==== Newton' | ||
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+ | The Momentum Principle (or Newton' | ||
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+ | $$\vec{F}_{net} = m\:\vec{a} = \dfrac{\Delta\vec{p}}{\Delta t}$$ | ||
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+ | where the last bit shows how Newton' | ||
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+ | $$\vec{a} = \dfrac{\Delta\vec{p}}{m\: | ||
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+ | where the last two equals signs hold only if the mass of the system is not changing. | ||
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+ | ==== Acceleration ==== | ||
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+ | // | ||
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+ | The acceleration can be defined in two ways and each is useful in different problems or ways of thinking. From Newton' | ||
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+ | $$\vec{a} = \dfrac{\vec{F}_{net}}{m}$$ | ||
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+ | Notice that this means that the acceleration of system always points in the direction of the net force (because mass is always a positive quantity). | ||
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+ | It can also be defined (as above) in terms of the change in velocity over time. If this change is calculated over a time interval ($\Delta t$), then you obtain the //average// acceleration, | ||
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+ | $$\vec{a}_{avg} = \dfrac{\Delta \vec{v}}{\Delta t} = \dfrac{\vec{v}_f - \vec{v}_i}{\Delta t}$$ | ||
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+ | If we allow the time interval to shrink ([[: | ||
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+ | $$\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}$$ | ||
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+ | The units of acceleration are meters per second per second ($\dfrac{m}{s^2}$). | ||
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+ | ==== 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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+ | **Finish this bit** |