# Ring Expansion

#### studiot

When considering shrinkage or swelling (whether by heat or other agent eg moisture uptake)

First divide into object and surroundings.

Then decide if only the object changes or are the surroundings also affected.

Then consider is the expansion free or constrained in any way.

Then find the longest dimension in the object (this may not be in a straight line)

Finally you can apply the linear expansion coefficient, which you may need to do in mutually perpendicular directions.

Can you now at least make a start on this question?

#### studiot

Here are some further hints

In this case the expansion is totally free.
The diameter D is the longest straight dimension this will increase to D(1+aΔT)
So the circumference (which is the longest dimension) will increase to πD(1+aΔT).

However the angle subtended to the centre by the gap cannot increase since a full circle must still contain 360 degrees.

So yes the gap will increase and this should be enough information to calculate this change.

• Razi

#### Razi

Dear studiot

Thanks for your hints , i have solved the question .

Best Regards