The ratio of L1 and L2 ,lengths of the sides of the rectangle when n = 2.24 is 2.0043
We use the centripetal acceleration definition,
[tex]a = \frac{v^2}{r}[/tex]
The relationship between angular and linear velocity
[tex]v=w^2r[/tex]
we substitute [tex]a = w^2 r[/tex]
The rectangular body rotates at an angle of w.
We locate the points, but the diagram is missing. In this case, the axis of rotation is in a corner called O, one of the adjacent corners is called A, and the opposite corner is called B.
the distance[tex]OB = L_2[/tex]
the distance [tex]AB = L_1[/tex]
It is indicated that the accelerations in A and B are related, so we substitute the acceleration value.
[tex]w^2 r_A = n r_B[/tex]
the distance from the each corner is
[tex]r_B = L_2\\\\ r_A =\sqrt{L_1^2+L_2^2}[/tex]
we substitute
[tex]\sqrt{L_1^2 + L_2^2} = n L_2[/tex]
[tex]L_1^2 + L_2^2 = n^2 L_2^2[/tex]
[tex]L_1^2= (n^2-1) L_2^2\\\\\frac{L_1^2}{L_2^2}=(n^2-1)\\\\\frac{L_1}{L_2}=\sqrt{(n^2-1)}[/tex]
When n=2.24
[tex]\frac{L_1}{L_2}=\sqrt{(2.24^2-1)}\\\\\frac{L_1}{L_2}=2.0043[/tex]
Thus, the ratios of length is 2.0043.
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