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ENGR5004 / Week 2
Dynamics Session 4 Worked example 1TutorialCurrent specThird5 min

ENGR5004 Dynamics Session 4 worked example 1 (slides 12-13) official answers

A car travels along a circular path of radius r=100r = 100 m. At the instant considered, its angular position measured from the centre of the circle is changing at θ˙=0.4\dot\theta = 0.4 rad/s with θ¨=0.2\ddot\theta = 0.2 rad/s2^2.

Using polar coordinates with origin at the centre, find the car's velocity and acceleration (components and magnitudes).

Formulas you may need
  • Polar velocity: v=r˙ ur+rθ˙ uθ\mathbf v = \dot r\,\mathbf u_r + r\dot\theta\,\mathbf u_\theta (learn this)
  • Polar acceleration: a=(r¨−rθ˙2)ur+(rθ¨+2r˙θ˙)uθ\mathbf a = (\ddot r - r\dot\theta^2)\mathbf u_r + (r\ddot\theta + 2\dot r\dot\theta)\mathbf u_\theta (learn this)