Answer:
2.07
Explanation:
Since you didn't supply the drawing, here is what I assumed:
A is the corner opposite the axis of rotation
B is one of the remaining two corners
L1 is the side between A & B
Centripetal acceleration is given by:
ac = v^2 / r = (v / r) * (v / r) * r…………1
Also angular speed is
w = v / r,………….2
Substituting (2) in (1) gives:
ac = (v / r) * (v / r) * r……….3
= (v / r)^2 * r
= w^2 * r
Therefore, the angular acceleration at A and at B are given by:
acA = w^2 * rA……..4
acB = w^2 * rB……..5
It is given that:
acA = n * acB…………6
Substituting (4) and (5) into (6) gives:
w^2 * rA = n * w^2 * rB ……….7==>
rA = n * rB……..8
In terms of the sides L1 and L2:
rA = sqrt (L1^2 + L2^2)…….9
and
rB = L2…………10
Considering (8):
n * L2 = sqrt (L1^2 + L2^2)………11
Squaring both sides:
n^2 * L2^2 = L1^2 + L2^2……….12
Dividing by L2^2:
n^2 = L1^2 / L2^2 + L2^2 / L2^2…….13
= (L1 / L2)^2 + 1 ==>
n^2 - 1 = (L1 / L2)^2 ………14==>
L1 / L2 = sqrt (n^2 - 1) ………15
= sqrt (2.30^2 - 1)
= 2.07. . . . . . <<<=== the value of the ratio L1 / L2 when n = 2.30
