Differences
This shows you the differences between two versions of the page.
Both sides previous revision Previous revision Next revision | Previous revisionLast revisionBoth sides next revision | ||
183_notes:curving_motion [2014/10/10 16:21] – pwirving | 183_notes:curving_motion [2018/05/29 21:06] – hallstein | ||
---|---|---|---|
Line 1: | Line 1: | ||
+ | Section 5.5, 5.6 and 5.7 in Matter and Interactions (4th edition) | ||
+ | |||
===== Modeling Curved Motion ===== | ===== Modeling Curved Motion ===== | ||
Line 63: | Line 65: | ||
$$\dfrac{d \hat{p}}{d t} = \dfrac{|\vec{v}|}{R} \hat{n}$$ | $$\dfrac{d \hat{p}}{d t} = \dfrac{|\vec{v}|}{R} \hat{n}$$ | ||
- | [{{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, | ||
Line 73: | Line 75: | ||
==== Relationship to the tangential and centripetal accelerations ==== | ==== Relationship to the tangential and centripetal accelerations ==== | ||
- | In your previous studies, you might have come across the [[http:// | + | In your previous studies, you might have come across the [[http:// |
$$\vec{F}_{net} = \vec{F}_{\parallel} + \vec{F}_{\perp}$$ | $$\vec{F}_{net} = \vec{F}_{\parallel} + \vec{F}_{\perp}$$ | ||
$$\vec{F}_{\parallel} | $$\vec{F}_{\parallel} | ||
- | 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 |
- | $$F_{\parallel} | + | $$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' | ||
+ | ==== Video of Bowling Ball Moving in a Circle ==== | ||
+ | |||
+ | In this video a bowling ball is forced to move in a circle by being struck with a sledgehammer. This video was originally collected by [[http:// | ||
+ | |||
+ | {{183_notes: | ||
+ | |||
+ | ==== Examples ==== | ||
+ | |||
+ | * [[: |