looking for partial matches between two sheets

I have two excel sheets as follow : sheet 1

       A          B
A  70811  spannar
B   3423  spanner
C   2334  looktide
Sheet 2  

      A      
A  spannar 123  
B  spanner 10 * 8 mm  
C  looktide

I want to know where in sheet1 I can find partial string matches with sheet2 and put the index match of sheet 2 in a new column beside the corresponding matched cell in sheet1

[KSSV]

How is sheet 2?

[Guillaume]

Missing from your question, and crucial, is your definition of a "partial string match"?

Looking at your example is it that strings in Sheet2 start with a string in Sheet 1. Or is it something more complex? (e.g., is annar a partial match for spannar 123?)