ENGR 220 Lecture 2: Linear Motion, and Cartesian and Polar Coordinates

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ENGR 220 Lecture 2 Linear Motion, and
Cartesian and Polar Coordinates

• Straight Line (Rectilinear) Motion

Diagram


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Integral Relationships for Straight Line
(Rectilinear) Motion
General Motion a(t) and v(t)
Acceleration as a function of position a(x)
Acceleration as a function of velocity a(v)
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Cartesian Coordinates

• 3D equations simplify easily to 2D equations
  which are used most
• Treat each direction independently for motion, as
  shown below
• In general xx(t) yy(t) zz(t)
  independently so rr(t) vv(t) aa(t)

2D Diagram
3D Diagram
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2D Coordinate Transformations

• How do you switch between ordinary Cartesian
  coordinates and angled Cartesian coordinates?

Diagram
Transformation
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Polar and Cylindrical Coordinates
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Example Ch 2.2 6 Accel vs. time plot shown.
Find change in position between t0s and t4s if
x(0) -4m/s.
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• Example Ch 2.2 13
• Sports car piston at 7000rpm moves 3.53in
  sinusoidally according to
• x(t) (3.53/2)sin(wt).
• Find max piston speed
• Find max piston accel in gs.

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Example Ch 2.2 20 Construct a coord
transformation array from i,j to b1,b2 for ?130
in system shown and express p4i-8j in terms of
b1,b2.
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Example Ch 2.3 2 Car at B travels towards
origin at constant speed v. What speed does
observer at A record (rB/A) with radar gun?
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Example Ch 2.3 15 Position of charged
particle is r at bt3 and ? ce-t. Find
equations for magnitude of velocity and
acceleration.