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| Both sides previous revision Previous revision | Last revisionBoth sides next revision | ||
| 183_notes:acceleration [2021/02/04 23:19] – [Newton's Second Law] stumptyl | 183_notes:acceleration [2021/02/04 23:22] – [Acceleration] stumptyl | ||
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| ==== Acceleration ==== | ==== Acceleration ==== | ||
| - | //Acceleration is a vector quantity that quantifies how quickly the velocity of a system is changing.// | + | **Acceleration** is a vector quantity that quantifies how quickly the velocity of a system is changing. |
| The acceleration can be defined in two ways and each is useful in different problems or ways of thinking. From Newton' | 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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| $$\vec{a} = \dfrac{\vec{F}_{net}}{m}$$ | $$\vec{a} = \dfrac{\vec{F}_{net}}{m}$$ | ||
| - | 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). | + | //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, | + | 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, |
| $$\vec{a}_{avg} = \dfrac{\Delta \vec{v}}{\Delta t} = \dfrac{\vec{v}_f - \vec{v}_i}{\Delta t}$$ | $$\vec{a}_{avg} = \dfrac{\Delta \vec{v}}{\Delta t} = \dfrac{\vec{v}_f - \vec{v}_i}{\Delta t}$$ | ||
| - | If we allow the time interval to shrink ([[: | + | 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 ($\dfrac{m}{s^2}$). | + | |
| ==== Why not just use change in momentum? ==== | ==== Why not just use change in momentum? ==== | ||