Rooks should be placed behind passed pawns

Why Rooks should be placed behind passed pawns – your pawns or your opponent’s pawns in the endgame?

Generally speaking, a piece is more active when it's on the opponent's side of the board.  So attacking an enemy pawn from the back simultaneously allows the rook to eye other features in the enemy's position, which may include cutting off the enemy king from further ranks.

Additionally, when you compare positions, a rook is decidedly less active in a blockading position.  Other than not eyeing any other enemy pawn or square, the rook also gets in the way of other friendly pieces that have to maneuver around it.

When supporting your own pawn, it's good behind because the rook itself won't obstruct the pawn's path to the queening square.  If the pawn is blockaded the supporting rook may be deemed passive, but because passed pawns are such a prominent / dangerous feature of a position, this sort of supporting role is often very effective for the friendly rook, even if it's doing little else than helping the pawn advance.

Whether the pawn is friend or foe, the rook will have more available sqaures each time the pawn advances.   A rook in front of a pawn will only lose mobility as the pawn moves closer to queening.

wafflemaster's points are all on the money.

The basic point is that a pawn that cannot be defended by another pawn is weak. This is why the ultimate goal of operations in a file is to get a R to the 7th rank. From that position a R is attacking enemy pawns from the side, where they have no defense. Simultaneously the R is hemming in the enemy K and keeping it on the back rank.

Additionally when a R is attacking pawns from the rear even pawns that form duos that can defend each other are paralyzed in their forward advance by the R. In other words, all pawns are weak when attacked from the rear by a R.