Differential arc segment

What is ds?

radius of curvature

What is p? (rho)

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

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

Italics v = Just the first derivative of position function

Difference between italics v and regular v

Formula: Normal Acceleration

Formula: Tangent 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

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?

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

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?