Project ForgeIn a rigid body in plane motion, the point R is accelerating with respect to point P at 10∠180° m/s². The triangle PQR has legs PQ=12, QR=16 (both along the coordinate axes at Q), and hypotenuse PR=20, with Q at the origin. If the instantaneous acceleration of point Q is zero, the acceleration (in m/s²) of point R is
- A8∠233°
- B10∠225°
- C10∠217°
- 8∠217°
Explanation
With Q=(0,0), P=(0,12), R=(16,0): a⃗R/P = −ω²(r⃗R−r⃗P) + α k̂×(r⃗R−r⃗P), with r⃗R−r⃗P=(16,−12). Setting this equal to the given (−10,0) and solving the two component equations gives ω²=0.4, α=−0.3. Since a⃗Q=0, a⃗R = a⃗R/Q = −ω²(16,0) + αk̂×(16,0) = (−6.4,0)+(0,−4.8) = (−6.4,−4.8), magnitude √(6.4²+4.8²)=8 m/s², direction atan2(−4.8,−6.4)≈217°. So a⃗R = 8∠217° m/s².
Source: GATE ME 2018 Session 2 (Set 2) (2018)
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