How to solve the 31st question?

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Answer 1 · 2018-03-14T10:40:45

See below.

Supposing that the B rod end glides without detaching from the wall, we have

$x_A = l cos theta$
$y_B = l sin theta$

and deriving

$dot x_A = v_A = -l sin theta dot theta$
$dot y_B = v_B = l cos theta dot theta$

and also

$ddot x_A = a_A = -l(dot theta)^2cos theta -lsin theta ddot theta$
$ddot y_B = a_B = -l (dot theta)^2sin theta+ l cos theta ddot theta$

Solving after eliminating $dot theta$ we have

$a_B =-(a_A Cot theta + (v_A^2 Csc^3 theta)/l)$

$ddot theta = -1/l^2(a_A l csc theta+ v_A^2 cot thetaCsc^2 theta)$