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ENGR5004 / Week 5
Dynamics L10 Worked exampleTutorialOld spec ENGR2162:210 min

ENGR216 Dynamics L10 worked example (slides 18-19) official answers

Just after a fan is switched on, the motor gives the blade an angular acceleration α=20e−0.6t\alpha = 20e^{-0.6t} rad/s2^2, where tt is in seconds. At t=0t = 0 the blade is at rest. The tip P of a blade is at r=0.5r = 0.5 m from the axis.

Find the speed and the magnitude of the acceleration of P at t=3t = 3 s, and the number of revolutions the blade has turned in the first 3 s.

Box fan; the blade tip P is 0.5 m from the axis of rotation.
Box fan; the blade tip P is 0.5 m from the axis of rotation.
Formulas you may need
  • Angular motion: ω=dθ/dt\omega = d\theta/dt, α=dω/dt\alpha = d\omega/dt (learn this)
  • Point on a body rotating about a fixed axis: v=ωrv = \omega r, at=αra_t = \alpha r, an=ω2ra_n = \omega^2 r (learn this)