The discussion focuses on calculating the center of mass of a semi-circular plate with a radius R and a density that varies linearly from 'd' at the center to '2d' at the circumference. The formula for the x-coordinate of the center of mass is given as Xcom = (∫xdm)/M. Participants suggest using polar coordinates to set up the integrals for mass and the first moment, emphasizing the need to express dm in terms of dx for accurate calculations.
PREREQUISITESStudents and professionals in physics, engineering, and mathematics who are involved in mechanics and material science, particularly those working on problems related to center of mass and variable density distributions.
What is your equation for density as a function of x? What is your equation for dm as a function of x?Neilquintal said:1. Find the centre of mass of a semi circular plate of radius R, the density of which linearly varies with distance, 'd' at the centre to a value '2d' at the circumference.
2. Xcom = (∫xdm)/M
3. I tried attempting the solution but I am not really knowing how to get dm in terms of dx