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Unformatted text preview: Curvature
Curvature measures the bend in a curve. 0Curvature is a . =
scalar. T v =
We will now use a new formula v(t)a(t) v() t
3 r =,t t ( t 32 t 2 , ) ex. ex. r= s s Find . ( ata t c i ) o n , t Do: r s c s . Find . ( i,oi t ns n ) t t t = , Acceleration Velocity has speed and direction. v() t v()=v() t t v() t Acceleration is the rate of change of velocity so a(t) has a component of rate of change of speed and also a component of rate of change of direction. T=
N= a a+ ( T a t TN ) = N aT is the tangential component of acceleration. is the normal component of acceleration. aN a= T dv d t = va v a =v = N 2 va v ex. r) t, t (= t
2 3 . Find aT and aN . ex. r 2,s 2 ( c 2 . Find aT t ) o i =s n t t , and aN . Do: r s c s . Find aT and aN . ( i,oi t ns n ) t t t = , ex. ex. t x, =r e = t ( tt e 3 t , y 3 ) = ex. N 0 ex. If a particle is moving on a path where a = is it moving in a straight line? ex. If a particle moves with constant speed can it be accelerating? ex. Let point P move along curve C with constant speed c. Let point Q move along C with speed 2c. Show that the magnitude of acceleration of Q is 4 times greater than that of P. ...
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This note was uploaded on 04/12/2008 for the course MATH 1224 taught by Professor Dontremember during the Fall '08 term at Virginia Tech.
 Fall '08
 DONTREMEMBER
 Geometry, Scalar

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