Swayed on the radio by the material (5)
I believe the answer is:
suede
'the material' is the definition.
(suede is a kind of material)
'swayed on the radio' is the wordplay.
'on the radio' indicates a 'sounds like' (homophone) clue.
'swayed' sounds like 'SUEDE'.
'by' acts as a link.
(Other definitions for suede that I've seen before include "Soft goatskin" , "Leather with flesh side rubbed to velvety nap" , "Undressed kidskin" , "Form of leather" , "Leather with velvety nap used in shoes and clothes" .)