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Unformatted text preview: 09/15/2010 Physics 201, Fall 2006, U.Wisconsin 1 3D Kinematics a71 The position , velocity , and acceleration of a particle in 3 dimensions can be expressed as: r = x i + y j + z k v = v x i + v y j + v z k ( i , j , k unit vectors ) a = a x i + a y j + a z k a71 We have already seen the 1D kinematics equations: x = x ( t ) v = dx dt a = dv dt = d 2 x dt 2 09/15/2010 Physics 201, Fall 2006, U.Wisconsin 2 3D Kinematics a71 For 3D, we simply apply the 1D equations to each of the component equations. a71 Which can be combined into the vector equations: dt r d v v r = x = x ( t ) v x = dx dt a x = dv x dt = d 2 x dt 2 y = y ( t ) v y = dy dt a y = dv y dt = d 2 y dt 2 z = z ( t ) v z = dz dt a z = dv z dt = d 2 z dt 2 2 2 dt r d a r r = k z j y i x r ˆ ˆ ˆ + + = r 09/15/2010 Physics 201, Fall 2006, U.Wisconsin 3 2D Kinematics Often 3D problems can be reduced to 2D problems : a71 Choose y axis to be along direction of acceleration a177 Choose x axis to be along the “other” direction of motion a71 Example : Throwing a baseball (neglecting air resistance) a177 Acceleration is constant (gravity) a177 Choose y axis up: a y = g a177 Choose x axis along the ground in the direction of the throw 09/15/2010...
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This note was uploaded on 01/04/2011 for the course PHYS 195 taught by Professor Anderson during the Fall '07 term at San Diego State.
 Fall '07
 Anderson
 Acceleration

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