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Jelly, (削除) 30 (削除ここまで) 23 bytes

OIḟ0μAI©Ṡḟ0ṂṭḢṠ$μ®ḟ0ṠEṭ

Try it online! Or see the test cases

All upper or all lower.
Returns a flag list [D, F, S]:
D: clockwise = 1 / anticlockwise = -1
F: centrifugal = 1 / centripetal = -1
S: spinning = 1 / not spinning = 0

• if S = 0 the other flags are still evaluated even though they carry no useful information.

###How?

OIḟ0μAI©Ṡḟ0ṂṭṠḢ$μ®ḟ0ṠEṭ - Main link: s
O - ordinals
 I - deltas (i.e. [a,b,c,...] -> [b-a,c-b,...])
 ḟ0 - filter out zeros
 - (call this Z)
 μ - start a new monadic chain (i.e. f(Z))
 A - absolute values
 I - deltas
 © - copy to register
 Ṡ - signs
 ḟ0 - filter out zeros
 Ṃ - minimum
 - (i.e. F = {centrifugal: 1; centripetal: -1})
 $ - last two links as a monad:
 Ḣ - head (Z)
 Ṡ - sign
 - (i.e. D = {clockwise: 1; anticlockwise: -1})
 ṭ - tack
 μ - start a new monadic chain (i.e. f([D,F]))
 ® - recall from register
 ḟ0 - filter out zeros
 Ṡ - signs
 E - all equal?
 - (i.e. S = {spinning: 1; not spinning: 0})
 ṭ - tack
 - (i.e. [D,F,S])