[Dynamics] 12.7 Curvilinear Motion: Normal and Tangential components

Differential arc segment
What is ds?
radius of curvature
What is p? (rho)
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Center of curvature
What is O’
Derivative of something with respect to time
What does time derivative mean
Unit normal
What does un mean?
Unit tangent
What does ut mean?
Expression: Acceleration vector
Expression: Acceleration vector
It is always tangent to path
Significance of velocity vector’s direction
Regular v = velocity vector
Italics v = Just the first derivative of position function
Difference between italics v and regular v
Formula: Normal Acceleration
Formula: Normal Acceleration
Formula: Tangent Acceleration
Formula: Tangent Acceleration
Equation:Magnitude of Acceleration
Equation:Magnitude of Acceleration
p(rho) = infinity
What is the curvature of a straight line?
Derivative of velocity magnitude (function) gives tangential acceleration
How are tangential component of acceleration and velocity related?
Is the time derivative in direction of velocity
Define transverse acceleration
Formula: Curvature
Formula: Curvature
5 m/s^2
A particle traveling in a circular path of radius 300m has an instantaneous velocity of 30 m/s and its velocity is increasing at a constant rate of 4m/s^2.
What is the magnitude of its total acceleration at this instant?
8.6 m/s
If a particle moving in a circular path of radius 5 m has a velocity function v=4t^2, what is the magnitude of its total acceleration at t=1?
inversely proportional to radius of curvature
How is normal acceleration related to curvature?
collinear
The directions of the tangential acceleration and velocity are always
plane in which the normal and tangential axis exist.
What is osculating plane?
Tangent to the path
What is the direction of velocity?
First time derivative of path function
What is the magnitude of velocity? (expression)
An = 0
what is the normal acceleration of a particle in a straight path?
An = v^2/p
At = 0
Constant circular motion: What are the components of acceleration?
The normal axis pointing to path’s center of curvature in 3d space
What is the principal normal?
The cross product vector perpendicular to both Un and Ut
What is the binormal axis?
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