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| 183_notes:curving_motion [2014/09/29 19:32] – pwirving | 183_notes:curving_motion [2014/10/10 16:21] – pwirving |
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| The motion of objects is not limited to [[183_notes:displacement_and_velocity|straight line motion]]. As you read earlier, [[183_notes:momentum_principle|forces can change the momentum of objects]] (including the direction of that momentum). These interactions can produce [[183_notes:localg|projectile motion]], [[183_notes:ucm|circular motion]], [[183_notes:springmotion|oscillations]], or more generalized trajectories. In these notes, you will read about how to model more generalized motion using the [[183_notes:momentum_principle|momentum principle]]. | The motion of objects is not limited to [[183_notes:displacement_and_velocity|straight line motion]]. As you read earlier, [[183_notes:momentum_principle|forces can change the momentum of objects]] (including the direction of that momentum). These interactions can produce [[183_notes:localg|projectile motion]], [[183_notes:ucm|circular motion]], [[183_notes:springmotion|oscillations]], or more generalized trajectories. In these notes, you will read about how to model more generalized motion using the [[183_notes:momentum_principle|momentum principle]]. |
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| | ==== Lecture Video ==== |
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| | {{youtube>wm2NbUDoAV0?large}} |
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| ==== The Derivative form of the Momentum Principle ==== | ==== The Derivative form of the Momentum Principle ==== |
| ==== Relationship to the tangential and centripetal accelerations ==== | ==== Relationship to the tangential and centripetal accelerations ==== |
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| In your previous studies, you might come acres the [[http://en.wikipedia.org/wiki/Acceleration#Tangential_and_centripetal_acceleration|tangential acceleration ($\vec{a}_{t}$) and the centripetal acceleration ($\vec{a}_{c}$)]]. This are directly connected to the definitions of the parallel and perpendicular components of the net force. You can write the net force as the sum of these parallel and perpendicular components, which arise from the tangential and centripetal accelerations. | In your previous studies, you might have come across the [[http://en.wikipedia.org/wiki/Acceleration#Tangential_and_centripetal_acceleration|tangential acceleration ($\vec{a}_{t}$) and the centripetal acceleration ($\vec{a}_{c}$)]]. These are directly connected to the definitions of the parallel and perpendicular components of the net force. You can write the net force as the sum of these parallel and perpendicular components, which arise from the tangential and centripetal accelerations. |
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| $$\vec{F}_{net} = \vec{F}_{\parallel} + \vec{F}_{\perp}$$ | $$\vec{F}_{net} = \vec{F}_{\parallel} + \vec{F}_{\perp}$$ |
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| The centripetal acceleration tells you how the direction of the object's motion changes, just as the perpendicular component of the net force is responsible for this directional change. | The centripetal acceleration tells you how the direction of the object's motion changes, just as the perpendicular component of the net force is responsible for this directional change. |
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