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ENGR5004 / Week 6
Dynamics L11 Worked example 1TutorialOld spec ENGR216Third8 min

ENGR216 Dynamics L11 worked example 1 (slides 12-13) official answers

A bar AB of length 1.5 m has rollers at both ends: roller A runs on the horizontal floor and roller B runs on a vertical wall to the left of A. At the instant shown the bar makes θ=30∘\theta = 30^\circ with the floor and roller A is moving to the right at 3 m/s.

Find the angular velocity of the bar and the velocity of B.

Bar AB of length 1.5 m; roller B on the vertical wall (upper left), roller A on the floor moving right at 3 m/s; the bar is at 30 degrees to the floor.
Bar AB of length 1.5 m; roller B on the vertical wall (upper left), roller A on the floor moving right at 3 m/s; the bar is at 30 degrees to the floor.
Formulas you may need
  • Relative velocity on a rigid body: vB=vA+ω×rB/A\mathbf v_B = \mathbf v_A + \boldsymbol\omega \times \mathbf r_{B/A} (learn this)
  • ωk×(xi+yj)=−ωy i+ωx j\omega\mathbf k \times (x\mathbf i + y\mathbf j) = -\omega y\,\mathbf i + \omega x\,\mathbf j (learn this)