Solution: Motion Along an Involute of a Circle The figure shows a particle moving along

Chapter 12, Problem 50

(choose chapter or problem)

Motion Along an Involute of a Circle shows a particle moving along a path modeled by The figure

\(\mathbf{r}(t)=\langle\cos \pi t+\pi t \sin \pi t, \sin \pi t-\pi t \cos \pi t\rangle\).

The figure also shows the vectors v(t) and a(t) for t = 1 and t = 2.

(a) Find \(a_{T}\) and \(a_{N}\) at t = 1 and t = 2.

(b) Determine whether the speed of the particle is increasing or decreasing at each of the indicated values of t. Give reasons for your answers.

Text Transcription:

r(t)=<cos pi t + pi t sin pi t, sin pi t - pi t cos pi t>

a_T

a_N