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(a) Find the curl of the centrifugal force. Comment on your result.

(a) Find the curl of the centrifugal force. Comment on your result.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Q2: Consider a cylindrical container that has water in it. The cylinder rotates about its axis at an angular speed of w. Upon rotation, the level of water will not remain flat; it will be curved such that it has an increasingly higher level as one moves away from the centre towards the walls of the cylinder. Consider a coordinate system that is fixed at the cylinder and rotates with at the same angular velocity. Take the z' axis to be aligned with the axis of the cylinder such that the angular velocity points along the +z' direction. The x'y' plane is, hence, parallel to the cylinder base. Place your coordinate system such that the lowest point on the water surface is at the origin. Solve the following questions: (a) Consider a point mass m that is located at the surface of the water at the coordinates (x', 0, z'). Draw a free body diagram of the mass indicating the directions of the weight, the "normal" force' (FN) from the rest of the water, and all inertial (fictitious) forces. (b) Use the fact that FN is perpendicular to the water surface and find the components of FN in terms of the components of the other forces that act on the particle. (c) Use your results of the previous part to express z' in terms of x'. Discuss your results. Q3: (a) Find the curl of the centrifugal force. Comment on your result. (b) Based on your result of the previous part, find the corresponding potential energy if relevant.
Transcribed Image Text:Q2: Consider a cylindrical container that has water in it. The cylinder rotates about its axis at an angular speed of w. Upon rotation, the level of water will not remain flat; it will be curved such that it has an increasingly higher level as one moves away from the centre towards the walls of the cylinder. Consider a coordinate system that is fixed at the cylinder and rotates with at the same angular velocity. Take the z' axis to be aligned with the axis of the cylinder such that the angular velocity points along the +z' direction. The x'y' plane is, hence, parallel to the cylinder base. Place your coordinate system such that the lowest point on the water surface is at the origin. Solve the following questions: (a) Consider a point mass m that is located at the surface of the water at the coordinates (x', 0, z'). Draw a free body diagram of the mass indicating the directions of the weight, the "normal" force' (FN) from the rest of the water, and all inertial (fictitious) forces. (b) Use the fact that FN is perpendicular to the water surface and find the components of FN in terms of the components of the other forces that act on the particle. (c) Use your results of the previous part to express z' in terms of x'. Discuss your results. Q3: (a) Find the curl of the centrifugal force. Comment on your result. (b) Based on your result of the previous part, find the corresponding potential energy if relevant.
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