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ENGR5004 / Week 8
Dynamics L16 Worked example 1TutorialOld spec ENGR2162:115 min

ENGR216 Dynamics L16 worked example 1 (slides 9-10) official answers

A motorised spool of mass 200 kg and radius of gyration kG=0.3k_G = 0.3 m about its centre G stands on the ground on its outer rims (radius 0.6 m). A cable is wound round its hub (radius 0.4 m); it leaves the top of the hub at A and runs horizontally to a fixed anchor B on a wall to the right. A motor applies an anticlockwise moment M=450M = 450 N m to the spool. The coefficient of kinetic friction between the spool and the ground is μk=0.1\mu_k = 0.1. Take g=9.81g = 9.81 m/s2^2.

Find the angular acceleration of the spool and the tension in the cable.

Spool with 0.6 m outer radius and 0.4 m hub on the ground; cable from the top of the hub (A) horizontally to anchor B on the right-hand wall; motor moment M = 450 N m anticlockwise.
Spool with 0.6 m outer radius and 0.4 m hub on the ground; cable from the top of the hub (A) horizontally to anchor B on the right-hand wall; motor moment M = 450 N m anticlockwise.
Formulas you may need
  • General plane motion: ∑Fx=m(aG)x\sum F_x = m(a_G)_x, ∑Fy=m(aG)y\sum F_y = m(a_G)_y, ∑MG=IGα\sum M_G = I_G\alpha (learn this)
  • Radius of gyration: IG=mkG2I_G = m k_G^2 (learn this)
  • Kinetic friction: F=μkNF = \mu_k N, opposing the slip (learn this)