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ENGR5004 / Week 5
Dynamics L9 Worked example 2TutorialOld spec ENGR2162:118 min

ENGR216 Dynamics L9 worked example 2 (slides 13-15) official answers

In a horizontal plane (neglect gravity), a smooth particle P of mass 0.08 kg is attached to an elastic cord from the fixed point O to P (stiffness k=30k = 30 N/m, unstretched length 0.25 m). A slotted arm rotating about O pushes P around the rim of a fixed circular disc of radius 0.4 m that passes through O, so that r=0.8sin⁡θr = 0.8\sin\theta m, where θ\theta is the arm angle. The arm rotates at a constant θ˙=5\dot\theta = 5 rad/s.

Find the forces that the slotted arm and the disc rim exert on the particle when θ=60∘\theta = 60^\circ.

Disc of radius 0.4 m with O on its rim; slotted arm through O at angle theta, rotating anticlockwise at 5 rad/s; particle P in the slot on the disc rim at distance r from O.
Disc of radius 0.4 m with O on its rim; slotted arm through O at angle theta, rotating anticlockwise at 5 rad/s; particle P in the slot on the disc rim at distance r from O.
Formulas you may need
  • Polar acceleration: ar=r¨−rθ˙2a_r = \ddot r - r\dot\theta^2, aθ=rθ¨+2r˙θ˙a_\theta = r\ddot\theta + 2\dot r\dot\theta (learn this)
  • Equations of motion: ∑Fr=mar\sum F_r = m a_r, ∑Fθ=maθ\sum F_\theta = m a_\theta (learn this)
  • Spring force: Fs=k(ℓ−ℓ0)F_s = k(\ell - \ell_0) (learn this)