A uniform disc of radius 45 cm has a circular hole of radius 15 cm cut out, so that the hole…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A uniform disc of radius has a circular hole of radius cut out, so that the hole touches the disc's edge. How far from the disc's centre is the centre of mass of what is left, and on which side?
Need a reminder? The key ideaShow
The centre of mass is the mass-weighted average position: , and the same for and . For a continuous body, . A hole can be treated as a negative mass.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. , hole radius , hole centre from the centre.
Plan. Full disc (mass at ) plus the hole (mass at ).
Step 1. .
Answer: from the centre, on the side away from the hole.
Check. Removing mass on one side must move the centre of mass to the other side. It does.
Watch out. Divide by the mass that is left, , not by the full disc's mass.
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