The bar AB in Fig. (a) is rigid. If it rotates through a small angle (in radians), assuming the change in length of the bar BC to be equal to b appears to be a valid approximation (Fig. (b)). Prove...

The bar
AB
in Fig. (a) is rigid. If it rotates through a small angle

(in radians), assuming the change in length of the bar
BC
to be equal to
b

appears to be a valid approximation (Fig. (b)). Prove that this is true. Assume that bar
AB
rotates through an arbitrary angle

(Fig. (c)) and solve for
L’
as a function of
. Then show that if

is sufficiently small that second- and higher-order terms can be neglected,
L‘ =
L
=
b
.

Strategy: Express
L’
as a Taylor series in terms of

and neglect terms of second and higher order.