Project ForgeIn a four-bar planar mechanism, AB=5cm, AD=4cm, and DC=2cm, with A and D as fixed pivots 4cm apart. In the configuration shown, both AB and DC are perpendicular to AD. Bar AB rotates with angular velocity 10 rad/s. The magnitude of angular velocity (in rad/s) of bar DC at this instant is
Explanation
Set A=(0,0), B=(0,5), D=(4,0), C=(4,2) (AB, DC both vertical). Velocity of B is horizontal (⊥AB), magnitude = ωAB×AB = 10×5 = 50 cm/s. The coupler BC = C−B = (4,−3), a 3-4-5 triangle. The rigid link BC preserves the velocity component along its own length at both ends: (vB)·(4/5) = (vC)·(4/5), since vC is also horizontal (⊥DC), giving vC = 50 cm/s. Then ωDC = vC/DC = 50/2 = 25 rad/s.
Source: GATE ME 2019 Session 1 (Set 1) (2019)
This question is part of a 15-day revision cycle — sign in and Project Forge will bring it back the day before you'd forget it.