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ENGR5004 / Week 7
ENGR216 2019 Q B2Past paperOld spec ENGR2162:125 marks30 min

ENGR216 Summer 2019 Q B2[VALID]

Figure B2 shows a disc and bar assembly. As the disc rolls along the plane surface, the bar slides along the plane surface. The disc is 1 m diameter and the bar is 1.2 m in length.

Figure B2: disc (centre O, contact point Q) with angular velocity 3 rad/s and angular acceleration 4 rad/s^2, both counter-clockwise; bar PR pinned to the disc at P (level with O) with end R on the surface.
Figure B2: disc (centre O, contact point Q) with angular velocity 3 rad/s and angular acceleration 4 rad/s^2, both counter-clockwise; bar PR pinned to the disc at P (level with O) with end R on the surface.
Formulas you may need
  • Rolling without slipping: vO=ωrv_O = \omega r, aO=αra_O = \alpha r, contact point has zero velocity (learn this)
  • Relative velocity: vB=vA+ω×rB/A\mathbf{v}_B = \mathbf{v}_A + \boldsymbol\omega\times\mathbf{r}_{B/A} (given in the 2019 Section B appendix; not on the 2026 sheet, so learn this)
  • Relative acceleration: aB=aA+α×rB/A−ω2rB/A\mathbf{a}_B = \mathbf{a}_A + \boldsymbol\alpha\times\mathbf{r}_{B/A} - \omega^2\mathbf{r}_{B/A} (given in the 2019 Section B appendix; not on the 2026 sheet, so learn this)
  • Instantaneous centre: ω=vA/rA/IC=vB/rB/IC\omega = v_A/r_{A/IC} = v_B/r_{B/IC} (given in the 2019 Section B appendix; not on the 2026 sheet, so learn this)
  1. (a)
    Determine the velocity of point Q.
    [3]Third
  2. (b)
    Determine the velocity of point O.
    [3]Third
  3. (c)
    Determine the velocity of point P.
    [3]
  4. (d)
    Determine the angular velocity of the bar PR, and also the linear velocity of the bar PR.
    [8]
  5. (e)
    Determine the acceleration of point R.
    [8]