If velocity V , acceleration A and force \Gamma are chosen as fundamental quantities, then the dimensional formula of angular momentum in terms of v, A and \Gamma would be
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L \propto V^{x} A^{y} F^{z} 
L = k V^{x} A^{y} F^{z}
Putting the dimensions in the above relation
\(\left[ML^{2}T^{-1}\right] = k \left[LT^{-1}\right]^{x} \left[LT^{-2}\right]^{y} \left[MLT^{-2}\right]^{z}\)
⇒ ⇒ \(\left[ML^{2}T^{-1}\right] = k \left[M^{z}L^{x+y+z}T^{-x-2y-2z}\right]\)
Comparing the powers of M, L and T
Z=1 …(i)
x + y + z = 2 …(ii)
-x - 2y - 2z = -1 …(iii)
On solving (i), (ii) and (iii) x = 3, y = -2, z = 1
So dimension of L in terms of v, A and f
\([L] = \left[ F v^{3} A^{-2} \right]\)
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