A-level Mathematics/OCR/M4

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This is the Mechanics 4 module of the A-level Mathematics book. This module assumes that you are familiar with the C1, C2, C3, C4, M1, M2 and M3 modules. Please post all questions to A-level Mathematics/Discussion.

Contents[edit]

  1. /Relative Motion0% developed  as of Dec 14, 2005
  2. Centre of Mass (Second Level)0% developed  as of Dec 14, 2005
  3. Moment of Inertia0% developed  as of Dec 14, 2005
  4. Rotation of a Rigid Body0% developed  as of Dec 14, 2005
  5. Simple Harmonic Motion (Second Level)0% developed  as of Dec 14, 2005

Formulae[edit]

By the end of this module you will be expected to have learnt the following formulae:

Relative Velocity[edit]

  • {}_P\!V_Q + {}_Q\!V_R = {}_P\!V_R

Angular Motion[edit]

For constant angular acceleration:

  •  \omega _1 = \omega _0 + \alpha t \,
  •  \theta = \omega _0 t + \frac{1}{2} \alpha t^2
  •  \theta = \frac{1}{2}(\omega _0 + \omega _1)t
  •  \omega _1^2 = \omega _0^2 + 2\alpha\theta
  •  \theta = \omega _1 t - \frac{1}{2} \alpha t^2
  • Angular momentum:  I\omega\,
  • Kinetic energy:  \frac{1}{2}I\omega ^2
  • Equation of motion:  C = I \ddot{\theta}
  • Work done by a constant couple:  W = C\theta\,