Centre of mass of a circular lamina..?

Anyone know how to do this? It's from the M2 revise book.

A think uniform circular disc has center, O, with radius 5cm and mass 5m. Particles of mass m and 3m are attached to the disc at the ends of the diameter AB. What is the center of mass from O?

Thanks

Reply 1

AlphaNumeric

By symmetry, you know the centre of mass of that system is going to be on the AB line.

You know the 3 centres of mass for the individual parts and where they are. There is a 1m mass at A (5cm from O), there is a 5m mass at the centre of AB, O, and there is a 3m mass at B (5cm from O).

You've now got a 1 dimensional problem. The total mass is 9m, and you want to find where it is along AB. Imagine AB was a rod and you wanted to find the centre of mass. Can you see how to do it now?