Final answer:
The question involves applying the concept of generalized spherical coordinates in n-dimensions to physics problems, including calculating coordinates in a unique coordinate system and analyzing the motion involving cylindrical shapes.
Step-by-step explanation:
The question pertains to finding formulas for generalized spherical coordinates in n-dimensions, which is a mathematical concept used widely in the field of physics, particularly in solving problems that deal with symmetrical three-dimensional fields like gravitation and electromagnetism. In physics, this might involve utilizing these coordinates to solve the Schrödinger's equation for spherically symmetric potentials or calculating the moment of inertia for complex shapes.
part (a), the question asks for the x coordinate in generalized spherical coordinates. The formula to find x in three-dimensional spherical coordinates is x = r sin θ cos φ. In n-dimensions, this might extend to more complex formulas involving additional angles representing orientation in higher-dimensional spaces.
Part (b) seems to be about applying these concepts to a practical physics problem involving rotation. The focus is on a coordinate system with the origin at the center of a cylinder, which might be relevant when analyzing the motion, such as rotation around the cylinder's axis or calculating the potential energy distribution in a cylindrical setup. Here, the mention of revolutions, the radius, and angular acceleration a suggest that we're dealing with rotational dynamics and kinematics.