In the shown rigid body undergoing plane motion, R accelerates relative to P at 10180\ m/s2. If instantaneous acceleration of Q is zero, find acceleration of R (m/s²).

GATE 2018 ME (ME2) – Question 39

Engineering Mechanics · Kinematics and dynamics of rigid bodies in plane motion · 2 marks · Multiple choice

In the shown rigid body undergoing plane motion, R accelerates relative to P at $10\angle180^\circ\ \mathrm{m/s^2}$. If instantaneous acceleration of Q is zero, find acceleration of R (m/s²).

Diagram for GATE 2018 ME (ME2) question 39

$8\angle233^\circ$
$10\angle225^\circ$
$10\angle217^\circ$
$8\angle217^\circ$

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Correct answer: (D) $8\angle217^\circ$

Explanation

Take Q = (0,0), P = (0,12), R = (16,0). Rigid-body acceleration gives $$\vec a_R-\vec a_P=\alpha\hat k\times(16\hat i-12\hat j)-\omega^2(16\hat i-12\hat j).$$ Comparing with $-10\hat i$ gives $12\alpha-16\omega^2=-10$ and $16\alpha+12\omega^2=0$. Thus $\omega^2=0.4$ and $\alpha=-0.3$. Since Q has zero acceleration, $\vec a_R=-6.4\hat i-4.8\hat j$, magnitude 8 and angle 216.87°. Answer **D**.