Question

The rod is slipping. Velocity and acceleration of one end of rod are given. Find the angular speed and the acceleration of corner P.

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Given
$tan\theta =\frac{3}{4}\Rightarrow sin\theta =\frac{3}{5};cos\theta =\frac{4}{5}$
$v=R\omega$
$\Rightarrow v_A=\left(5sin\theta \right)\omega$
$\Rightarrow \omega =\frac{v_A}{5sin\theta }=\frac{10}{5\left(\frac{3}{5}\right)}=\frac{10}{3}rad/s$
Along the length of the rod, $a_{A}cos\theta =a_{B}sin\theta$
$\Rightarrow a_B=a_A\frac{cos\theta }{sin\theta }$
$=\frac{\left(2\right)\left(\frac{4}{5}\right)}{\left(\frac{3}{5}\right)}=\frac{8}{3}m/s^2$