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.

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 is 0 the other flags are still evaluated even though they carry no useful information.

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 (X)
 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])

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])

Jelly, 30 bytes

3L·ḟ0ṠE
ÑṠḟ0Ṃ
ÑAI
OIḟ0
ÇṠḢ;2L·;Ñ

TryItOnline
Or see the test cases (with a slight change as the very last Ñ would point to the new main link)

(My lack of chaining skill is probably costing a few bytes here)
All upper or all lower.
Returns a flag list [D, F, S]:
S: spinning = 1 / not spinning = 0
F: centrifugal = 1 (circular = 0) centripetal = -1
D: clockwise = 1 / anticlockwise = -1

3L·ḟ0ṠE - Link 1, isSpinning: s
3L· - call link 3 as a monad with s
 ḟ0 - filter out zeros
 Ṡ - sign
 E - all equal?

ÑṠḟ0Ṃ - Link 2, centrifugal(-1), circular(0) or centripetal(1): s
Ñ - call next link (3) as a monad with s
 Ṡ - sign (+1 for positive changes, -1 for negative changes, 0 for no change)
 ḟ0 - filter out zeros (ignore these for cases like "IRIS")
 Ṃ - minimum (will be the only value for spinning words)
 - (circular words like "DAD", now excluded, yield min([])=0)
ÑAI - Link 3, absolute change of moves over alphabet: s
Ñ - call next link (4) as a monad with s
 A - absolute
 I - differences
OIḟ0 - Link 4, non-zero moves over alphabet: s
O - ordinal cast
 I - differences
 ḟ0 - filter out zeros
ÇṠḢ;2L·;Ñ - Main link: s
Ç - call last link (4) as a monad with s
 Ṡ - sign
 Ḣ - head (clockwise / anticlockwise: 1 / -1)
 ; ; - concatenate
 2L· - call link (2) as a monad with s
 Ñ - call next link (1) as a monad with s

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

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 (X) 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])