183_notes:curving_motion

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
Next revision		 Previous revision
Next revisionBoth sides next revision
183_notes:curving_motion [2015/09/27 15:49] – [Relationship to the tangential and centripetal accelerations] caballero183_notes:curving_motion [2016/08/17 18:07] – waterso8
Line 78: Line 78:
 $$\vec{F}_{\parallel}  = m\vec{a}_{t} = m{a}_{t}\hat{p} \qquad \vec{F}_{\perp} = m\vec{a}_{c} = m{a}_{c}\hat{n}$$ $$\vec{F}_{\parallel}  = m\vec{a}_{t} = m{a}_{t}\hat{p} \qquad \vec{F}_{\perp} = m\vec{a}_{c} = m{a}_{c}\hat{n}$$
  
-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 (or opposite it in the case of negative acceleration). 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.
  
 $$F_{\parallel}  = m{a}_{t} = \dfrac{d|\vec{p}|}{dt} = \dfrac{d|m\vec{v}|}{dt} = m\dfrac{d|\vec{v}|}{dt} \qquad\longrightarrow\qquad {a}_{t} = \dfrac{d|\vec{v}|}{dt}$$ $$F_{\parallel}  = m{a}_{t} = \dfrac{d|\vec{p}|}{dt} = \dfrac{d|m\vec{v}|}{dt} = m\dfrac{d|\vec{v}|}{dt} \qquad\longrightarrow\qquad {a}_{t} = \dfrac{d|\vec{v}|}{dt}$$
Line 87: Line 87:
  
 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.
 +
 +==== 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://paer.rutgers.edu|Eugenia Etkina and David Brookes]]. 
 +
 +{{183_notes:bowlingball.mp4}}
 +
 +==== Examples ====
 +
 +  * [[:183_notes:examples:videoswk6|Video Example: Change in momentum (parallel and perpendicular) of an orbit]]
  • 183_notes/curving_motion.txt
  • Last modified: 2021/03/04 12:56
  • by stumptyl