Kinematics fundamentals
By: Sunil Singh
Online: < http://cnx.org/content/col10348/1.29>
This selection and arrangement of content as a collection is copyrighted by Sunil Singh.
It is licensed under the Creative Commons Attribution License: http://creativecommons.org/licenses/by/2.0/
Collection structure revised: 2008/09/28
For copyright and attribution information for the modules contained in this collection, see the " Attributions" section at the end of the collection.
Kinematics fundamentals
Table of Contents
We require an observer to identify motion
Frame of reference and observer
We need to change our mind set
Is there an absolute frame of reference?
1.2. Coordinate systems in physics
Rectangular (Cartesian) coordinate system
Vector addition : graphical method
Vector addition : Analytical method
Representation of a vector in component form
Vector addition : Algebraic method
Scalar product in component form
Component as scalar (dot) product
Attributes of scalar (dot) product
Differentiation and dot product
1.9. Scalar product (application)
Representative problems and their solutions
Condition of perpendicular vectors
Scalar product of a vector with itself
Cross product in component form
Geometric meaning vector product
Attributes of vector (cross) product
1.11. Vector product (application)
Representative problems and their solutions
Position Vector in component form
Motion types and position vector
Displacement and Position vector
Displacement and dimension of motion
Interpreting change of position
Position – time plot and average velocity
Instantaneous velocity and position - time plot
Position vector in rectilinear motion
Vector interpretation and equivalent system of scalars
The nature of velocity – time plot
Area under velocity – time plot
1.17. Rectilinear motion (application)
Representative problems and their solutions
Interpretation of displacement - time plot
Representative problems and their solutions
Acceleration in terms of position vector
2.2. Understanding acceleration
Velocity, acceleration and force
External force and possible scenarios
2.3. Acceleration and deceleration
“Increase” and “decrease” of vectors quantities
Graphical interpretation of negative vector quantities describing motion
2.4. Accelerated motion in one dimension
Nature of acceleration in one dimensional motion
Graphs of one dimensional motion
Area under acceleration - time plot
Understanding constant acceleration
Graphical interpretation of equations of motion
Equations of motion in component form
Equivalent scalar system of equations of motion
2.6. Constant acceleration (application)
Representative problems and their solutions
Differentiation and Integration methods
Rectilinear motion with constant acceleration
2.7. One dimensional motion with constant acceleration
Equation of motion for one dimensional motion with constant acceleration
Additional equations of motion
Displacement in a particular second
Interpretation of equations of motion
Constant acceleration (force) is applied in the direction of velocity
Constant acceleration (force) is applied in the opposite direction of velocity
2.8. Graphs of motion with constant acceleration
Nature of coefficient of squared term
Acceleration is positive (in the reference direction)
Acceleration is negative (opposite to the reference direction)
2.9. Vertical motion under gravity
2.10. Vertical motion under gravity (application)
Representative problems and their solutions
Displacement in a particular second
2.11. Non-uniform acceleration
Velocity and acceleration is expressed in terms of time “t
Velocity and acceleration is expressed in terms of time “x”
Acceleration in terms of velocity
Obtaining expression of velocity in time, “t”
Obtaining expression of velocity in time, “x”
3.1. Relative velocity in one dimension
Relative motion in one dimension
Acceleration of the point object
Interpretation of the equation of relative velocity
Equation with reference to earth
Evaluating relative velocity by making reference object stationary
Direction of relative velocities
Relative velocity .vs. difference in velocities
3.2. Relative velocity in one dimension(application)
Representative problems and their solutions
3.3. Relative velocity in two dimensions
Relative motion in two dimensions
Acceleration of the point object
Interpretation of the equation of relative velocity
Equation with reference to earth
Evaluation of equation using analytical technique
3.4. Relative velocity in two dimensions (application)
Representative problems and their solutions
Velocity of an individual object
3.5. Analysing motion in a medium
Concept of independence of motion
Shortest interval of time to cross the stream
Direction to reach opposite point of the stream
The velocity to reach opposite point of the stream
Motion of an object in a medium
3.6. Resultant motion (application)
Representative problems and their solutions
Minimum time, distance and speed
Chapter 4. Accelerated motion in two dimensions
Projectile motion and equations of motion
Equations of motion in vertical direction
Equations of motion in horizontal direction
Equation of the path of projectile
Projectile motion (application)
Representative problems and their solutions
Change in angles during motion
Kinetic energy of a projectile
Change in the direction of velocity vector
Maximum height reached by the projectile, H
Equation of projectile motion and range of projectile
Situations involving projectile motion
Clearing posts of equal height
Determining attributes of projectile trajectory
Features of projectile motion (application)
Representative problems and their solutions
Height attained by a projectile
Projectile motion with wind/drag force
Projection from a higher level
Projectile thrown in horizontal direction
Projectile thrown at an angle with horizontal direction
Projectile thrown up at an angle with horizontal direction
Projectile thrown down at an angle with horizontal direction
Projectile motion types (application)
Representative problems and their solutions
Projectile motion on an incline
Coordinates along incline (x) and perpendicular to incline (y)
Coordinates in horizontal (x) and vertical (y) directions
Projectile motion on an incline (application)
Representative problems and their solutions
Elastic collision with the incline
Projectile motion on two inclines
Relative motion of projectiles
Relative velocity of projectiles