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183_notes:curving_motion [2014/09/24 17:40] – [A change in direction] caballero | 183_notes:curving_motion [2014/09/24 17:51] – [Relationship to the tangential and centripetal accelerations] caballero |
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$$\vec{F}_{net,\perp} = |\vec{p}|\dfrac{d \hat{p}}{d t} = \dfrac{|\vec{p}||\vec{v}|}{R} \hat{n} =\dfrac{mv^2}{R} \hat{n} $$ | $$\vec{F}_{net,\perp} = |\vec{p}|\dfrac{d \hat{p}}{d t} = \dfrac{|\vec{p}||\vec{v}|}{R} \hat{n} =\dfrac{mv^2}{R} \hat{n} $$ |
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| ==== 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. |
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| $$\vec{F}_{net} = \vec{F}_{\parallel} + \vec{F}_{\perp}$$ |
| $$\vec{F}_{\parallel} = m\vec{a}_{t} = m{a}_{t}\hat{p} \qquad \vec{F}_{\perp} = m\vec{a}_{c} = m{a}_{c}\hat{n}$$ |