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Understanding Mechanics: Motion Vocabulary and Equations

Explore key concepts like displacement, velocity, acceleration, and kinematics in mechanics. Learn the difference between scalar and vector quantities, distance versus displacement, and speed versus velocity. Discover how to calculate velocity, acceleration, and interpret ticker-tape diagrams. Dive into position versus time graphs and velocity versus time graphs to understand motion analysis. Gain insights into free fall and acceleration due to gravity. Engage with examples and equations to master kinematics in a detailed study of object motion.

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Understanding Mechanics: Motion Vocabulary and Equations

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  1. Ch. 2 - 3 Displacement, Velocity, and Acceleration

  2. Vocabulary • Mechanics – the study of the motion of objects • Kinematics – Describing the motion of objects with words, diagrams, graphs and mathematical equations

  3. Vocabulary • Vector– a quantity (thing that can be measured) which contains both a size (magnitude) and direction. • Ex: • Scalar – a quantity which is completely described with a magnitude and has no associated direction • Ex: • Some things are by nature a scalar or a vector, some are DEFINED to be a scalar or a vector

  4. Distance vs. Displacement vs. Position • Distance – total path length travelled • Scalar • Displacement – length from starting to ending point. • vector • Points FROM starting point TO ending point • Position – measured from origin (you set coordinate system!)

  5. Calculating Displacement

  6. Speed vs. Velocity • Speed – “How fast” = distance / time • Defined to be a scalar • Equation for AVERAGE speed: • Velocity – “how fast and in what direction” = DISPLACEMENT/time • Defined as a vector (needs direction!) • Equation for AVERAGE velocity:

  7. Calculating Velocity

  8. Acceleration • “how quickly something speeds up” AND/OR “how quickly something changes direction” • Equation for average acceleration: • Direction of acceleration (in 1-D)

  9. Ticker-Tape Diagrams (aka particle diagrams) • Dot represents the “center of mass” of the object • Like a strobe light picture – equal intervals of time occur between each recorded dot • Examples:

  10. Vector Diagrams (aka motion diagrams) • Use a picture of the object (sometimes a dot) along with vectors to represent the motion of an object • Length of arrow represents size of vector quantity • Examples:

  11. Position vs. Time Graphs • Position on y-axis • Time on x-axis • Example with constant velocity • Slope of line =

  12. Position vs. time graphs - examples

  13. Velocity vs. Time graphs • Velocity on y-axis; time on x-axis • Example – constant acceleration: • Slope of velocity vs. time graph =

  14. Velocity vs. Time Graph - examples

  15. Velocity vs. Time graph – finding displacement • Displacement = AREA between line and x-axis • Area above the x-axis is positive displacement, area below is negative displacement • Example

  16. Equations of Kinematics • Velocity with average accel. equation

  17. Equations of Kinematics • Displacement as area under position vs. time graph:

  18. Equations of Kinematics • Final velocity squared

  19. Kinematics Example: Dimensional Analysis

  20. Kinematics Example:

  21. Kinematics Example:

  22. Free-Fall An object is in free fall if its motion is only being affected by gravity - air resistance is not a factor (negligible) - not being propelled by its own power source - generally assumed to be on earth, unless otherwise specified - can be going up OR down! Examples:

  23. Acceleration Due to Gravity • Galileo’s Experiment (*demo/video demo) • Acceleration due to gravity (on Earth) =

  24. Free Fall ex: Object is dropped

  25. Free Fall ex: Obj. is thrown upward

  26. Free Fall ex: Obj. is thrown downward

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