Answer to Question #273035 in Differential Geometry | Topology for Samson

Question

Suppose

u=rcos(wt)i+rsin(wt)j where r and w are constants, find the vector velocity

Answer 1

Since $U= r*cos(W*t)i + r*sin(W*t)j$ it implies that the velocity is $\frac{du}{dt}$ that is

$$\frac{du}{dt}=r*\frac{d(cos(W*t ))}{dt}i+r*\frac{d(sin(W*t))}{dt}j$$

This implies

$$\frac{du}{dt}=r*W(-sin(W*t))i +r*W(cos(W*t))j$$

Hence,

$$\frac{du}{dt} =(-rW*sin(Wt))i +(rWcos(Wt))j$$

Which happens to be the vector velocity.