c1 = W + W′α, c2 = W + W′β,
(1)
where α, β are numerical factors depending on the external shape; and if the C.G. is moving with velocity V at an angle φ with the axis, so that the axial and broadside component of velocity is u = V cos φ, v = V sin φ, the total momentum F of the medium, represented by the vector OF at an angle θ with the axis, will have components, expressed in sec. ℔,
| F cos θ = c1 | u | = (W + W′α) | V | cos φ, F sin θ = c2 | v | = (W + W′β) | V | . |
| g | g | g | g |
(2)
Suppose the body is kept from turning as it advances; after t seconds the C.G. will have moved from O to O′, where OO′ = Vt; and at O′ the momentum is the same in magnitude as before, but its vector is displaced from OF to O′F′.
For the body alone the resultant of the components of momentum
| W | V | cos φ and W | V | sin φ is W | V | sec. ℔, |
| g | g | g |
(3)
acting along OO′, and so is unaltered.