CH4 2d Motion.notebook
PHYS 2325 Motion in 2D
1
Sep 275:16 PM
Chapter 4
Motion in Two Dimensions
Oct 78:15 AM
4.1 The Position, Velocity, and Acceleration Vectors
4.2 Two Dimensional Motion with Constant Acceleration
4.3 Projectile Motion
4.4 Analysis Model: Particle in Uniform Circular Motion
4.5 Tangential and Radial Acceleration
4.6 Relative Velocity and Relative Acceleration
Sep 275:16 PM
Kinematics in Two Dimensions
•
Will study the vector nature of position,
velocity and acceleration in greater detail
•
Will treat projectile motion and uniform
circular motion as special cases
•
Discuss relative motion
Introduction
Sep 275:16 PM
Position and Displacement
•
The position of an object
is described by its position
vector,
.
•
The
displacement
of
the object is defined as the
change in its position.
•
Sep 275:16 PM
General Motion Ideas
•
In two‐ or three‐dimensional kinematics,
everything is the same as in one‐dimensional
motion except that we must now use full vector
notation.
•
Positive and negative signs are no longer sufficient to
determine the direction.
Section 4.1
Sep 275:16 PM
Average Velocity
•
The average velocity is the ratio of the displacement to
the time interval for the displacement.
•
The direction of the average velocity is the direction of
the displacement vector.
•
The average velocity between points is
independent of
the path
taken.
•
This is because it is dependent on the displacement, which is also
independent of the path.
Section 4.1
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PHYS 2325 Motion in 2D
2
Oct 78:30 AM
Sep 275:16 PM
Instantaneous Velocity
•
The instantaneous velocity is the limit of
the average velocity as
Δ
t
approaches zero.
•
As the time interval becomes smaller, the
direction of the displacement approaches
that of the line tangent to the curve.
Sep 275:16 PM
Instantaneous Velocity, cont
•
The direction of the instantaneous velocity
vector at any point in a particle’s path is along a
line tangent to the path at that point and in the
direction of motion.
•
The magnitude of the instantaneous velocity
vector is the speed.
•
The speed is a scalar quantity.
Section 4.1
Sep 275:16 PM
Average Acceleration
•
The average acceleration of a particle as it
moves is defined as the change in the
instantaneous velocity vector divided by the time
interval during which that change occurs.
Sep 275:16 PM
Average Acceleration, cont
•
As a particle moves, the
direction of the change in
velocity is found by vector
subtraction.
•
The average acceleration is
a vector quantity directed
along
.
Section 4.1
Sep 275:16 PM
Instantaneous Acceleration
•
The instantaneous acceleration is the
limiting value of the ratio
as Δ
t
approaches
zero.
•
The instantaneous equals the derivative of the
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 Spring '08
 ERSKINE/TSOI
 Velocity, Sep, 2D

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