Is the relationship ∆ϕ 1 + ∆ϕ 2 = ∆ϕ 2 + ∆ϕ 1 valid if ∆ϕ 1 and ∆ϕ 2 refer to different axes of rotation? Is it valid if they refer to different rotations about the same axis?

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Kevin Nash · Answer

It can be seen from the figure above that the book is rotated about the x axis twice by 20° . One can observe that the commutative law of addition remains validated when the axis of rotation is kept same.

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Is the relationship ∆ϕ 1 + ∆ϕ 2 = ∆ϕ 2 + ∆ϕ 1 valid if ∆ϕ 1 and ∆ϕ 2 refer to different axes of rotation? Is it valid if they refer to different rotations about the same axis?

Is the relationship ∆ϕ₁ + ∆ϕ₂ = ∆ϕ₂ + ∆ϕ₁ valid if ∆ϕ₁ and ∆ϕ₂ refer to different axes of rotation? Is it valid if they refer to different rotations about the same axis?

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Is the relationship ∆ϕ 1 + ∆ϕ 2 = ∆ϕ 2 + ∆ϕ 1 valid if ∆ϕ 1 and ∆ϕ 2 refer to different axes of rotation? Is it valid if they refer to different rotations about the same axis?

Is the relationship ∆ϕ1 + ∆ϕ2 = ∆ϕ2 + ∆ϕ1 valid if ∆ϕ1 and ∆ϕ2 refer to different axes of rotation? Is it valid if they refer to different rotations about the same axis?

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Is the relationship ∆ϕ₁ + ∆ϕ₂ = ∆ϕ₂ + ∆ϕ₁ valid if ∆ϕ₁ and ∆ϕ₂ refer to different axes of rotation? Is it valid if they refer to different rotations about the same axis?