The center of mass of a uniform circular disc with a hole is determined by the equations x² + y² ≤ 1 for the disc and (x - 1/2)² + y² ≥ (1/16) for the hole. The center of mass is calculated to be at the coordinates (-1/30, 0). The discussion highlights the importance of accurately interpreting the equations and emphasizes that the center of mass is a precise point rather than a range. Misunderstandings regarding the problem's wording and the need for visual representation are also addressed.
PREREQUISITESStudents in physics or mathematics, particularly those tackling problems related to center of mass, geometry, and calculus. This discussion is beneficial for anyone looking to enhance their problem-solving skills in geometric contexts.
Aliasa said:
SteamKing said:
Yes, but can you find the area? This is a disk with a hole in it. It would be a good idea to at least draw a picture of the "hole bounded by the equations x^2 + y^2 ≤ 1 and (x - 1/2)^2 + y^2 ≥ (1/16)." Those boundaries are circles. Can you graph the circles?Aliasa said:
You are misunderstanding the question. The metal template is very precisely defined by the two equations; there is no range of possible shapes and sizes. The centre of mass is an exact point. The two equations together define the metal surface, the hole is where there is metal missing.Aliasa said:
Aliasa said:
Yes. That's correct. Nice job.Aliasa said:
