pattern - What is a Rotary Club Word™?

_{This is in the spirit of the What is a Word™/Phrase™ series started by JLee with a special brand of Phrase™ and Word™ puzzles.}

If a word conforms to a special rule, I call it a Rotary Club Word™.
Use the following examples below to find the rule.

$$\begin{array}{|c|c|}\hline \bbox[yellow]{\textbf{Rotary Club Words }^™}& \bbox[yellow]{\textbf{Not Rotary Club Words }^™}\\ \hline \text{ ANT }&\text{ FLY }\\ \hline \text{ ASH }&\text{ CINDERS }\\ \hline \text{ DEN }&\text{ CAVE }\\ \hline \text{ CHAR }&\text{ BURN }\\ \hline \text{ INCH }&\text{ METER }\\ \hline \text{ DYED }&\text{ TINTED }\\ \hline \text{ RELY }&\text{ TRUST }\\ \hline \text{ LOYAL }&\text{ TRUE }\\ \hline \text{ ANGLE }&\text{ VEER }\\ \hline \text{ CEDAR }&\text{ PINE }\\ \hline \text{ ELBOW }&\text{ KNEE }\\ \hline \text{ VERSE }&\text{ POETRY }\\ \hline \text{ STABLE }&\text{ UNSTABLE }\\ \hline \text{ ALPINE }&\text{ LOFTY }\\ \hline \text{ ERRING }&\text{ PERFECT }\\ \hline \text{ STRIPE }&\text{ SOLID }\\ \hline \text{ TOOLBARS }&\text{ ICONS }\\ \hline \text{ PRINTOUTS }&\text{ HARDCOPY }\\ \hline \end{array}$$

And, if you want to analyze, here is a CSV version:

Rotary Club Words™,Not Rotary Club Words™
ANT,FLY
ASH,CINDERS
DEN,CAVE
CHAR,BURN
INCH,METER
DYED,TINTED
RELY,TRUST
LOYAL,TRUE

ANGLE,VEER
CEDAR,PINE
ELBOW,KNEE
VERSE,POETRY
STABLE,UNSTABLE
ALPINE,LOFTY
ERRING,PERFECT
STRIPE,SOLID
TOOLBARS,ICONS
PRINTOUTS,HARDCOPY

The puzzle relies on the series' inbuilt assumption, that each word can be tested for whether it is a Rotary Club Word™ without relying on the other words.

These are not the only examples of Rotary Club Words™, many more exist.

Answer

Every Rotary Club Word can be:

Converted to another word by rotating part of the end to the beginning:

So

ANT -> TAN
ASH -> HAS
DEN -> END
CHAR -> ARCH
INCH -> CHIN
DYED -> EDDY
RELY -> LYRE
LOYAL -> ALLOY
ANGLE -> GLEAN
CEDAR -> ARCED

ELBOW -> BOWEL
VERSE -> SEVER
STABLE -> ABLEST
ALPINE -> PINEAL
ERRING -> RINGER
STRIPE -> RIPEST
TOOLBARS -> BARSTOOL
PRINTOUTS -> OUTSPRINT