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ENGR5004 / Week 9
Dynamics L17 Worked example 1TutorialOld spec ENGR2162:212 min

ENGR216 Dynamics L17 worked example 1 (slides 11-13) official answers

A 40 kg disc of radius 0.8 m and radius of gyration kG=0.6k_G = 0.6 m stands on a horizontal floor. A cord wrapped around its rim leaves the top of the disc (point A) horizontally and is connected to a spring of stiffness k=10k = 10 N/m anchored to a wall on the left. A constant clockwise couple M=15M = 15 N m is applied, so the disc rolls to the right, away from the wall, without slipping. It starts from rest with the spring unstretched.

Find the angular velocity of the disc when its centre G has moved 0.5 m.

Disc of radius 0.8 m rolling on the floor; a cord from the top point A runs left to a spring k = 10 N/m anchored to the wall; clockwise couple 15 N m.
Disc of radius 0.8 m rolling on the floor; a cord from the top point A runs left to a spring k = 10 N/m anchored to the wall; clockwise couple 15 N m.
Formulas you may need
  • Principle of work and energy: T1+∑U1−2=T2T_1 + \sum U_{1-2} = T_2 (learn this)
  • Kinetic energy in plane motion: T=12mvG2+12IGω2T = \tfrac12 m v_G^2 + \tfrac12 I_G\omega^2, IG=mkG2I_G = m k_G^2 (learn this)
  • Work of a couple U=MΔθU = M\Delta\theta; work of a spring U=−12k(s22−s12)U = -\tfrac12 k(s_2^2 - s_1^2) (learn this)
  • Rolling without slipping: vG=ωrv_G = \omega r, ΔsG=rΔθ\Delta s_G = r\Delta\theta (learn this)