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Do you mean, can they be in either order? Yes. It's the order of the integral signs that defines the order of integration (inside first).Quarlep said:
Find average velocity of a sphere which expands and moves
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SUMMARY
The discussion focuses on calculating the average velocity of a spherical shell that expands and moves, specifically addressing the velocities involved: expansion velocity (v) and movement velocity (v'). Participants clarify that while expansion velocities can cancel out in certain contexts, the average velocity remains dependent on the movement velocity v'. The kinetic energy of the shell is also discussed, emphasizing that energy is a scalar quantity and does not simply cancel out like vector quantities. The conversation highlights the need for proper mathematical treatment, including the use of double integrals in spherical coordinates for accurate calculations.
PREREQUISITES- Understanding of vector and scalar quantities in physics
- Familiarity with kinetic energy concepts and equations
- Knowledge of spherical coordinates and double integrals
- Basic principles of symmetry in physics problems
- Study the derivation of kinetic energy in spherical coordinates
- Learn about the application of double integrals in physics problems
- Explore the concept of center of mass and its implications in motion
- Review vector addition and cancellation in the context of physics
Students studying physics, particularly those focusing on mechanics and energy concepts, as well as educators looking for examples of complex motion and energy calculations involving spherical objects.