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183_notes:curving_motion [2014/10/06 18:06] – caballero | 183_notes:curving_motion [2015/09/27 15:49] – [Relationship to the tangential and centripetal accelerations] caballero | ||
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$$\dfrac{d \hat{p}}{d t} = \dfrac{|\vec{v}|}{R} \hat{n}$$ | $$\dfrac{d \hat{p}}{d t} = \dfrac{|\vec{v}|}{R} \hat{n}$$ | ||
- | [{{183_notes: | + | [{{183_notes: |
where the unit vector, $\hat{n}$, always points inward towards the turn. For more general trajectories, | where the unit vector, $\hat{n}$, always points inward towards the turn. For more general trajectories, | ||
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==== Relationship to the tangential and centripetal accelerations ==== | ==== Relationship to the tangential and centripetal accelerations ==== | ||
- | In your previous studies, you might come acres the [[http:// | + | In your previous studies, you might have come across |
$$\vec{F}_{net} = \vec{F}_{\parallel} + \vec{F}_{\perp}$$ | $$\vec{F}_{net} = \vec{F}_{\parallel} + \vec{F}_{\perp}$$ | ||
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The direction of each of these accelerations is the same as their corresponding forces. The tangential acceleration is tangent to the path, and this points in the $\hat{p}$ direction. The centripetal acceleration is perpendicular to the path and points in the $\hat{n}$ direction. You can use the magnitudes of each force component to determine formulae for the accelerations. | The direction of each of these accelerations is the same as their corresponding forces. The tangential acceleration is tangent to the path, and this points in the $\hat{p}$ direction. The centripetal acceleration is perpendicular to the path and points in the $\hat{n}$ direction. You can use the magnitudes of each force component to determine formulae for the accelerations. | ||
- | $$F_{\parallel} | + | $$F_{\parallel} |
The tangential acceleration tells you how the speed of the object changes, just as the parallel component of the net force is responsible for this speeding up and slowing down. | The tangential acceleration tells you how the speed of the object changes, just as the parallel component of the net force is responsible for this speeding up and slowing down. | ||
- | $$F_{\perp} | + | $$F_{\perp} |
The centripetal acceleration tells you how the direction of the object' | The centripetal acceleration tells you how the direction of the object' | ||
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