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Understanding Free Fall and Vector Addition: Physics Concepts Explained

Explore the concept of free fall under gravity and learn about vectors and two-dimensional motion. Discover properties of vectors, vector notation, vector addition, and subtraction. Understand components of a vector and learn how to add vectors algebraically and graphically. This comprehensive guide simplifies complex physics principles for easier comprehension.

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Understanding Free Fall and Vector Addition: Physics Concepts Explained

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  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 earth’s 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 AF_0306.swf

  11. Notes about Vector Addition • Vectors obey the Commutative Law of Addition • The order in which the vectors are added doesn’t 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 θ 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 θ with respect to the positive x-axis

  16. Adding Vectors Algebraically • Grandma’s 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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