91Ó°ÊÓ

A bug is crawling outward along the spoke of a wheel that lies along a radius of the wheel. The bug is crawling at 1 unit per second and the wheel is rotating at 1 radian per second. Suppose the wheel lies in the yz-plane with center at the origin, and at time \(t=0\) the spoke lies along the positive \(y\) -axis and the bug is at the origin. Find a vector function \(\boldsymbol{r}(t)\) for the position of the bug at time t.

Describe a situation in which the normal component of acceleration is 0 and the tangential component of acceleration is non-zero. Is it possible for the tangential component of acceleration to be 0 while the normal component of acceleration is non-zero? Explain. Finally, is it possible for an object to move (not be stationary) so that both the tangential and normal components of acceleration are 0? Explain.