Refers specifically to the shuttlecock used in the traditional Japanese game hanetsuki (羽根突き), similar to badminton but played without a net.
See also: 羽根つき
We played hanetsuki with a shuttlecock during the New Year holidays.
battledore; hagoita paddle
Compound of 羽 (は, 'feather') and 子 (ご, a diminutive suffix). The reading ご for 子 is a common rendaku form.