This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: The acceleration is a ( t ) = d v dt = & 4 sin (2 t ) i + 4 cos (2 t ) j . The unit tangent vector is T ( t ) = 1 v ( t ) v ( t ) = 1 2 (2 cos (2 t ) i + 2 sin (2 t ) j ) = cos (2 t ) i + sin (2 t ) j . Also d T dt = & 2 sin (2 t ) i + 2 cos (2 t ) j and & & & & d T dt & & & & = q ( & 2 sin (2 t )) 2 + (2 cos (2 t )) 2 = 2 so the curvature is & ( t ) = 1 v ( t ) & & & & d T dt & & & & = 1 2 (2) = 1 . The tangential component of acceleration is a T ( t ) = dv dt = d dt (2) = 0 and the normal component of acceleration is a N ( t ) = & ( t ) ( v ( t )) 2 = (1) (2) 2 = 4 . 2...
View
Full Document
 Fall '10
 Ellermeyer
 Math, Vector Space, Acceleration, Cos, Euclidean space, Osculating circle

Click to edit the document details