Motion%20in%20One%20Dimension - PowerPoint PPT Presentation

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Motion%20in%20One%20Dimension

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Chapter 2 Motion in One Dimension – PowerPoint PPT presentation

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Title: Motion%20in%20One%20Dimension


1
Chapter 2
  • Motion in One Dimension

2
Free Fall
  • All objects moving under the influence of only
    gravity are said to be in free fall
  • All objects falling near the earths surface fall
    with a constant acceleration
  • Galileo originated our present ideas about free
    fall from his inclined planes
  • The acceleration is called the acceleration due
    to gravity, and indicated by g

3
Acceleration due to Gravity
  • Symbolized by g
  • g 9.8 m/s²
  • g is always directed downward
  • toward the center of the earth

4
Non-symmetrical Free Fall
  • Need to divide the motion into segments
  • Possibilities include
  • Upward and downward portions
  • The symmetrical portion back to the release point
    and then the non-symmetrical portion

5
Combination Motions
6
Chapter 3
  • Vectors and
  • Two-Dimensional Motion

7
Vector Notation
  • When handwritten, use an arrow
  • When printed, will be in bold print A
  • When dealing with just the magnitude of a vector
    in print, an italic letter will be used A

8
Properties of Vectors
  • Equality of Two Vectors
  • Two vectors are equal if they have the same
    magnitude and the same direction
  • Movement of vectors in a diagram
  • Any vector can be moved parallel to itself
    without being affected

9
Adding Vectors
  • When adding vectors, their directions must be
    taken into account
  • Units must be the same
  • Graphical Methods
  • Use scale drawings
  • Algebraic Methods
  • More convenient

10
Graphically Adding Vectors, cont.
  • Continue drawing the vectors tip-to-tail
  • The resultant is drawn from the origin of A to
    the end of the last vector
  • Measure the length of R and its angle
  • Use the scale factor to convert length to actual
    magnitude

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11
Notes about Vector Addition
  • Vectors obey the Commutative Law of Addition
  • The order in which the vectors are added doesnt
    affect the result

12
Vector Subtraction
  • Special case of vector addition
  • If A B, then use A(-B)
  • Continue with standard vector addition procedure

13
Components of a Vector
  • A component is a part
  • It is useful to use rectangular components
  • These are the projections of the vector along the
    x- and y-axes

14
Components of a Vector, cont.
  • The x-component of a vector is the projection
    along the x-axis
  • The y-component of a vector is the projection
    along the y-axis
  • Then,

15
More About Components of a Vector
  • The previous equations are valid only if ? is
    measured with respect to the x-axis
  • The components can be positive or negative and
    will have the same units as the original vector
  • The components are the legs of the right triangle
    whose hypotenuse is A
  • May still have to find ? with respect to the
    positive x-axis

16
Adding Vectors Algebraically
  • Grandmas house
  • Add all the x and y-components
  • This gives Rx and Ry
  • Use the Pythagorean Theorem to find the magnitude
    of the Resultant
  • Use the inverse tangent function to find the
    direction of R
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