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ENGR5004 / Week 7
Dynamics L13 Worked example 2TutorialOld spec ENGR216Third6 min

ENGR216 Dynamics L13 worked example 2 (slides 17-18) official answers

A gear of pitch radius 0.3 m rolls without slipping on a fixed horizontal rack. At the instant shown it has a clockwise angular velocity ω=12\omega = 12 rad/s and a clockwise angular acceleration α=6\alpha = 6 rad/s2^2. Point A is at the top of the gear, directly above the centre O.

Find the acceleration of point A.

Gear of radius 0.3 m rolling on a fixed rack, clockwise omega = 12 rad/s and alpha = 6 rad/s^2; A is the top point; a_O is horizontal.
Gear of radius 0.3 m rolling on a fixed rack, clockwise omega = 12 rad/s and alpha = 6 rad/s^2; A is the top point; a_O is horizontal.
Formulas you may need
  • Rolling without slipping: aO=αra_O = \alpha r (centre moves on a straight line) (learn this)
  • Relative acceleration: aA=aO+α×rA/O−ω2rA/O\mathbf a_A = \mathbf a_O + \boldsymbol\alpha \times \mathbf r_{A/O} - \omega^2\mathbf r_{A/O} (learn this)