shake & move
掉 centers on vigorous back-and-forth motion: shaking something or moving it with force. The given meaning "shake & move" captures this single idea of causing something to oscillate or shift.
掉 combines the hand radical 扌 with 卓, which likely contributes the sound. The character is associated with shaking or moving by hand, but the exact historical development of the 卓 component in this context is uncertain.
The hand radical 扌 beside 卓 suggests a hand shaking something vigorously. Picture a hand gripping a tall, table-like object (卓 can mean eminent or table) and shaking it back and forth.
For トウ, imagine shaking a tall tower (tower -> トウ) with your hand: the tower sways as you shake it, and the sound "tow" cues the reading トウ.
final effort; final spurt