Acceleration is the time derivative of velocity. Because velocity is a vector, i

Question

Acceleration is the time derivative of velocity. Because velocity is a vector, it can change in two ways: the length (magnitude) can change and/or the direction can change. The latter type of change has a special name, the centripetal acceleration. In this problem we consider a mass moving in a circle of radius R with angular velocity w, r(t)=R[cos(wt)x + sin(wt)y] = Rcos(wt)x + Rsin(wt)y
What is the velocity of the mass at a time ? You can work this out geometrically with the help of the hints, or by differentiating the expression for given in the introduction.
Express this velocity in terms of R, w, t, and the unit vectors x and y.

Explanation / Answer

solve it by using the velocity and acceleration in differential form

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