ENSC2004 - Lecture 16

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ENSC2004 - Lecture 15
Conservation of Momentum - Slides

Conservation of Linear Momentum

• Only the impulse of external forces can cause a change in momentum
  • Internal forces do not matter, as they occur as pairs
    $J=\Delta p=m(v_f-v_i)$
• When the sum of external impulses is zero:
  $\sum m_i(v_i{)}_1=\sum m_i(v_i{)}_2$
• Typically applied when particles collide or interact

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Angular Momentum - Slides

Angular Momentum

• Angular momentum of a particle about $O$ is defined as the “moment” of the particles linear motion about $O$
  ${\text{H}}_O=r\times \text{m}v$

  
  $r$ in this diagram would be $d$

• Angular moment is not the same as the linear momentum!
  $\sum {\text{M}}_O=r\times F={\dot{\text{H}}}_O$
  A dot above a character represents a time derivative

• If something starts at rest, its initial angular momentum = 0

Principle of Angular Impulse and Momentum

By integrating the equation above, we can get:
$(H_O{)}_1+\sum {\int }_{t_1}^{t_2}{M}_{O}dt=(H_O{)}_2$

• This is known as the principle of angular impulse and momentum
  • $\sum {\int }_{t_1}^{t_2}{M}_{O}dt$ → angular impulse
• Angular momentum is sometimes represented with $L$

Conservation of Angular Momentum

• If sum of angular impulses is zero, angular momentum is conserved
  $(H_O{)}_1=(H_O{)}_2$
  e.g. if a particle is only subject to forces pointing towards $O$

  
  A good example of this in practice, would be the tension force acting upon a ball swinging around a pole from a rope

• Typically you will use: $0=m_a\cdot v_a\cdot r_a-m_b\cdot v_b\cdot r_b$

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ENSC2004 - Lecture 17