Let the position of a point p in three dimensions be given by the vector r-cx, y,z) in rectangular (or cartesian) coordinates. the same position can be specified by cylindrical polar coordinates, p, φ, z, which are defined as follows: let p' denote the projection of p onto the xy plane: that is, p' has cartesian coordinates (x, y, 0). then rho and φ are defined as the two-dimensional polar coordinates of p' in the xy plane, while z is the third cartesian coordinate, unchanged. (a) make a sketch to illustrate the three cylindrical coordinates. give expressions for rho, φ, z in terms of the cartesian coordinates x, y, z. explain in words what rho is ("rho is the distance of p from are many variants in notation. for instance, some people use r instead of p. explain why this use of r is unfortunate. (b) describe the three unit vectors rho, φ,2 and write the expansion of the position vector r in terms of these unit vectors. (c) differentiate your last answer twice to find the cylindrical components of the acceleration a ř of the particle. to do this, you will need to know the time derivatives of rho and φ. you could get these from the corresponding two-dimensional results (1.42) and ( 1.46), or you could derive them directly as in problem 1.48. ").