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ENGR5004 / Week 8
Dynamics L15 Worked example 1TutorialOld spec ENGR2162:210 min

ENGR216 Dynamics L15 worked example 1 (slides 10-13) official answers

A uniform slender horizontal rod of mass 15 kg and length 0.9 m is supported by a pin at O, 0.6 m from its left end (0.3 m from its right end), and by a vertical cord attached to its left end. The cord is cut. Take g=9.81g = 9.81 m/s2^2 and IG=ml2/12I_G = ml^2/12.

Find the angular acceleration of the rod and the reactions at the pin O just after the cord is cut.

Horizontal rod, 0.6 m to the left of pin O and 0.3 m to the right; G is 0.15 m left of O; a vertical cord at the left end is cut.
Horizontal rod, 0.6 m to the left of pin O and 0.3 m to the right; G is 0.15 m left of O; a vertical cord at the left end is cut.
Formulas you may need
  • Fixed-axis rotation: ∑Fn=mω2rG\sum F_n = m\omega^2 r_G, ∑Ft=mαrG\sum F_t = m\alpha r_G, ∑MO=IOα\sum M_O = I_O\alpha (learn this)
  • Parallel-axis theorem: IO=IG+mrG2I_O = I_G + m r_G^2; slender rod IG=112ml2I_G = \tfrac{1}{12}ml^2 (learn this)