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ENGR5004 / Week 6
Dynamics L12 Worked example 2TutorialOld spec ENGR216Third6 min

ENGR216 Dynamics L12 worked example 2 (slides 14-16) official answers

A wheel of outer radius 0.8 m has a hub of radius 0.3 m. The wheel rolls on its hub, without slipping, along a horizontal rail (the outer rim overhangs the rail), and its centre C moves to the right at vC=2v_C = 2 m/s. Point A is on the hub at the same height as C, on the right-hand side; point B is at the top of the outer rim.

Find the velocities of A and B at this instant.

Wheel (outer radius 0.8 m) rolling on its 0.3 m hub on a rail; C moves right at 2 m/s; A on the hub level with C, B at the top of the rim. A plan view shows the hub running in a slot.
Wheel (outer radius 0.8 m) rolling on its 0.3 m hub on a rail; C moves right at 2 m/s; A on the hub level with C, B at the top of the rim. A plan view shows the hub running in a slot.
Formulas you may need
  • Rolling without slipping: the contact point is the IC, vC=ωrv_C = \omega r (learn this)
  • vP=ω×rP/IC\mathbf v_P = \boldsymbol\omega \times \mathbf r_{P/IC} (learn this)