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DynamicsEGCE 302
Spring 2016
California State University, Fullerton
Department of Civil and Environmental Engineering
Nagi Abo-Shadi, PhD, PE, SE, PEng
Chapter : Particle Kinematics
Curvilinear Motion of Particles
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Chapter 11 Particle Kinematics
Curvilinear Motion of Particles
Curvilinear Motion:Any motion other than straight line
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For small r = ds, v is
tangent to the curve
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Acceleration
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System of Coordinates
Magnitude and direction of velocity and acceleration
are determined with respect reference axis.
This is based on the coordinate system used; such as:
1. Rectangular Coordinates
2. Normal / Tangential Coordinates
3. Radial / Transverse Coordinates
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1. Rectangular Coordinates (x, y ,z)
Position vector
Velocity vector
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1. Rectangular Coordinates (x, y ,z)
Position vector
Acceleration vector
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Example
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= cos 25
= sin 25
= 0 = d cos 5= 0 = - d sin 5
= d cos 5=
-ds
in5
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cos 25
X-Direction (Uniform motion)
= d cos 5=
-ds
in5
Eq 1
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Y-Direction (Uniform acceleration)
- sin 5 = 0 + sin 25 t +
= d cos 5=
-ds
in5
Eq 2
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Solve Eq 1 and Eq 2 for (d) and (t)
= 726.06 ft
cos 25
Eq 1
- sin 5 = 0 + sin 25 t +
Eq 2
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Relative Motion
Position vector rB/Aof B relative to A
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Example
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Uniform Rectilinear Motion
As Given Shifted
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Two (2) ways of dealing with this problem:
(1)
= 180 25 = 155
+ + = 180 = =/
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(2)
= += +
= - += 48 = 109.5 km/hr
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(2)
= +
= +
= 0 +
= 48 = 20.3 km/hr
=
