Motion in a Plane

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Motion in a Plane Readings Chapter 4
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Kinematics in Two Dimensions
Average velocity
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Kinematics in Two Dimensions Instantaneous
Velocity
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Kinematics in Two Dimensions
(motion along a line)
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Kinematics in Two Dimensions Instantaneous
Acceleration
Average acceleration
Instantaneous acceleration
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Kinematics in Two Dimensions Instantaneous
Acceleration
Motion along a line acceleration results in
change of speed (the magnitude of
velocity) Motion in a plane acceleration can
change the speed (the magnitude of velocity) and
the direction of velocity.
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A Projectile is an object that moves in two
dimensions (in a plane) under the influence of
only the gravitational force.
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A Projectile is an object that moves in two
dimensions with free fall acceleration
- motion along x-axis with zero acceleration
constant velocity


- motion along y-axis free fall motion with
constant acceleration
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Example Find the distance AB
Point A -
Point B -
then
then
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Motion in a Circle
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Kinematics in Two Dimensions Uniform Circular
Motion Motion with Constant Speed
The speed (magnitude of velocity) is the same
Period
The position of the particle is characterized by
angle (or by arc length)
Arc length
where angle is in RADIANS
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Example
What is the arc length for
if
Arc length
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Kinematics in Two Dimensions Uniform Circular
Motion Motion with Constant Speed
The speed (magnitude of velocity) is the same
Then
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Uniform Circular Motion
Then
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Positive angle
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Uniform Circular Motion Acceleration
Direction of acceleration is the same as
direction of vector (toward the center)
The magnitude of acceleration
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Uniform Circular Motion Acceleration
centripetal acceleration
The magnitude of acceleration