Updating column so that it contains the row position

Question

This is the content table:

ContentID | CategoryID | Position | Other1 | Other2
===================================================
1         | 1          | NULL     | abcd   | efgh
2         | 1          | NULL     | abcd   | efgh
3         | 1          | NULL     | abcd   | efgh
4         | 2          | NULL     | abcd   | efgh
5         | 2          | NULL     | abcd   | efgh
6         | 2          | NULL     | abcd   | efgh

These are the queries I'll be running:

SELECT ContentID FROM content WHERE CategoryID = 1 ORDER BY Position
SELECT ContentID FROM content WHERE CategoryID = 2 ORDER BY Position

Now I want to implement move up, move down, move to top and move to bottom function for content. All I need to do is to populate the Position column with numbers:

ContentID | CategoryID | Position
=================================
1         | 1          | 1
2         | 1          | 2
3         | 1          | 3
4         | 2          | 1
5         | 2          | 2
6         | 2          | 3

Is it possible to achieve this via single query in MySQL? Something like:

UPDATE content
SET Position = <ROW_NUMBER>
WHERE CategoryID = 1
ORDER BY Position

UPDATE content
SET Position = <ROW_NUMBER>
WHERE CategoryID = 2
ORDER BY Position

Answer 1

This should work

update 
content,
(
  select 
  @row_number:=ifnull(@row_number, 0)+1 as new_position,
  ContentID 
  from content
  where CategoryID=1
  order by position
) as table_position
set position=table_position.new_position
where table_position.ContentID=content.ContentID;

But I would prefer to apply this first, to unset user defined variable

set @row_number:=0;

Added by Mchl:

You can do that in one statement like this

update 
content,
(
  select 
  @row_number:=ifnull(@row_number, 0)+1 as new_position,
  ContentID 
  from content
  where CategoryID=1
  order by position
) as table_position,
(
  select @row_number:=0
) as rowNumberInit
set position=table_position.new_position
where table_position.ContentID=content.ContentID;