ENSC2004 - Lecture 12

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ENSC2004 - Lecture 11
Relative Motion - Slides

Relative Motion

Relative Position

• The absolute positions of two particles A and B with respect to the fixed $x,y,z$-reference frame are given by $r_A$ and $r_B$
• The position of B relative to A is represented by:
  $r_{B/A}=r_B-r_A$

Relative Velocity

• The velocity of B relative to A is represented by:
  $v_{B/A}=v_B-v_A$
  OR:
  $v_B=v_A+v_{B/A}$
  Note: $v_{B/A}=-v_{A/B}$

Relative Acceleration

• The acceleration of B relative to A is represented by:
  $a_{B/A}=a_B-a_A$
  OR:
  $a_B=a_A+a_{B/A}$

Laws of Sines and Cosines

• Can be used to solve vector problems “graphically”

Law of Sines: $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$
Law of Cosines: $c^2=a^2+b^2-2ab\cos C$

You can choose to either use trigonometry to solve problems or to break vectors into components for basic arithmetic

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Dependent Motion - Slides

Dependent Motion

• In kinematics problems, motion of one object can depend on another

To find an equation relating velocities, determine the relation in position coordinates and then derive the expression

• You don’t need to consider line segments that don’t change
  As they derive to 0!
• See examples in slides

Full Method:

1. Define position coordinates from fixed datum lines, along the path of each particle
2. Relate the position coordinates to the cord length
3. If a system contains more than one cord, relate position of a point on one cord to a point on another cord
   • Separate equations are written for each cord
4. Differentiate the position coordinate equation(s) to relate velocities and accelerations

Helpful video:

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ENSC2004 - Lecture 13