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183_notes:acceleration [2014/07/10 20:35] – caballero | 183_notes:acceleration [2014/07/10 20:51] – caballero | ||
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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' | ||
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The Momentum Principle (or Newton' | The Momentum Principle (or Newton' | ||
- | $$\vec{F}_{net} = m\:\vec{a} = \dfrac{\Delta\vec{p}}{Delta t}$$ | + | $$\vec{F}_{net} = m\:\vec{a} = \dfrac{\Delta\vec{p}}{\Delta t}$$ |
where the last bit shows how Newton' | where the last bit shows how Newton' | ||
- | $$\vec{a} = \dfrac{\Delta\vec{p}}{m\: | + | $$\vec{a} = \dfrac{\Delta\vec{p}}{m\: |
where the last two equals signs hold only if the mass of the system is not changing. | where the last two equals signs hold only if the mass of the system is not changing. | ||
+ | |||
+ | ==== Acceleration ==== | ||
+ | |||
+ | // | ||
+ | |||
+ | The acceleration can be defined in two ways and each is useful in different problems or ways of thinking. From Newton' | ||
+ | |||
+ | $$\vec{a} = \dfrac{\vec{F}_{net}}{m}$$ | ||
+ | |||
+ | 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). | ||
+ | |||
+ | 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, | ||
+ | |||
+ | $$\vec{a}_{avg} = \dfrac{\Delta \vec{v}}{\Delta t} = \dfrac{\vec{v}_f - \vec{v}_i}{\Delta t}$$ | ||
+ | |||
+ | If we allow the time interval to shrink ([[: | ||
+ | |||
+ | $$\vec{a} = \lim_{\Delta t \rightarrow 0}\vec{a}_{avg} = \lim_{\Delta t \rightarrow 0}\dfrac{\Delta \vec{v}}{\Delta t} = \dfrac{d\vec{v}}{dt}$$ | ||
+ | |||
+ | The units of acceleration are meters per second per second ($\dfrac{m}{s^2}$). | ||
+ |