CurvatureCurvature measures the bend in a curve. κ≥0. Curvature is a scalar. κ=′T vWe will now use a new formula κ=vt(29×at(29vt(293ex. rt(29=t2, t3, t2
ex. rt(29=acost, asintFind κ.
Do: rt(29=sint, cost, sint. Find κ.
AccelerationVelocity has speed and direction. vt(29=vt(29vt(29vt(29Acceleration is the rate of change of velocity so at( 29has a component of rate of change of speed and also a component of rate of change of direction.T=N=at(29=aTT+aNNaTis the tangential component of acceleration.aNis the normal component of acceleration.aT=dvdt=v⋅avaN=v2κ=v×av
ex. If a particle is moving on a path where aN=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.