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Vectors and Scalars (Tutorial)

Learn about vectors and scalars in physics, their properties, and applications through examples and problems. Understand vector addition, subtraction, and non-collinear vectors. Includes polar coordinates.

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Vectors and Scalars (Tutorial)

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  1. Vectors and Scalars (Tutorial) Eng. Ahmed Eng. Abdulslam

  2. Scalarand Vectors • A SCALAR is any quantity in physics that has MAGNITUDE, but NOT a direction associated with it. • Such as { speed } • A VECTOR is any quantity in physics that has BOTH MAGNITUDE and DIRECTION. • Such as {Acceleration }

  3. Applications of Vectors VECTOR ADDITION – If 2 similar vectors point in the SAME direction, add them. VECTOR SUBTRACTION - If 2 vectors are going in opposite directions, subtract them.

  4. Applications of Vectors • Example: A man walks 54.5 meters east, then 30 meters west. Calculate his displacement relative to where he started? 54.5 m, E - 30 m, W 24.5 m, E

  5. Applications of Vectors • Problem: Car moves 80 Km east, then 30 Km west. After that it moves again 50 Km east . Calculate its displacement relative to where it started? 100 Km , East

  6. Non-Collinear Vectors When 2 vectors are perpendicular, you must use the Pythagorean theorem. Key of chapter

  7. The direction? We follow these graphs : N W of N E of N # North # South # East # West N of E N of W E W S of W S of E W of S E of S S

  8. Non-Collinear Vectors Example: A boat moves with a velocity of 15 m/s, N in a river which flows with a velocity of 8.0 m/s, west. Calculate the boat's resultant velocity with respect to due north. 8.0 m/s, W 15 m/s, N Rv q The Final Answer : 17 m/s, @ 28.1 degrees West of North

  9. Non-Collinear Vectors Example : A plane moves with a velocity of 63.5 m/s at 32 degrees South of East. Calculate the plane's horizontal and vertical velocity components. x 32 y 63.5 m/s X = 53.85 m/s , east . Y= 33.64 m/s , south .

  10. Non-Collinear Vectors • Problem : R = 14.3 Km Angle : 65° N of E

  11. Vectors and Polar Coordinates

  12. R R q Ry q Ry f f q Rx Rx R Rx Rx q f Ry Ry R Four Quadrants Q = 180 - f Q = f Q = 180 + f Q = 360 - f Problem : suppose : f = 40 o what are theq ?

  13. Problem : X = 86.60 m Y= - 50 m

  14. Thank You

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