Edexcel M5 2002 June — Question 6

Exam BoardEdexcel
ModuleM5 (Mechanics 5)
Year2002
SessionJune
TopicSimple Harmonic Motion

  1. Show that the moment of inertia of the rod about the edge of the table is \(\frac { 7 } { 3 } m a ^ { 2 }\). The rod is released from rest and rotates about the edge of the table. When the rod has turned through an angle \(\theta\), its angular speed is \(\dot { \theta }\). Assuming that the rod has not started to slip,
  2. show that \(\dot { \theta } ^ { 2 } = \frac { 6 g \sin \theta } { 7 a }\),
  3. find the angular acceleration of the rod,
  4. find the normal reaction of the table on the rod. The coefficient of friction between the rod and the edge of the table is \(\mu\).
  5. Show that the rod starts to slip when \(\tan \theta = \frac { 4 } { 13 } \mu\)
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