Vectors Vectors and Scalars Vector Quantity which requires
- Slides: 19
Vectors
Vectors and Scalars • Vector: Quantity which requires both magnitude (size) and direction to be completely specified – 2 m, west; 50 mi/h, 220 o – Displacement; Velocity • Scalar: Quantity which is specified completely by magnitude (size) – 2 m; 50 mi/h – Distance; Speed
Vector Representation • Print notation: A – Sometimes a vector is indicated by printing the letter representing the vector in bold face
Mathematical Reference System 90 o y 180 o Angle is measured counterclockwise wrt positive x-axis x 270 o 0 o
Equal and Negative Vectors
Vector Addition A + B = C (head to tail method) B + A = C (head to tail method) A + B = C (parallelogram method)
Addition of Collinear Vectors
Adding Three Vectors
Vector Addition Applets • Visual Head to Tail Addition • Vector Addition Calculator
Subtracting Vectors
Vector Components Vertical Component Ay= A sin Horizontal Component Ax= A cos
Signs of Components
Components ACT • For the following, make a sketch and then resolve the vector into x and y components. Ay Ax Bx By Ax = (60 m) cos(120) = -30 m Bx = (40 m) cos(225) = -28. 3 m Ay = (60 m) sin(120) = 52 m By = (40 m) sin(225) = -28. 3 m
(x, y) to (R, ) • Sketch the x and y components in the proper direction emanating from the origin of the coordinate system. • Use the Pythagorean theorem to compute the magnitude. • Use the absolute values of the components to compute angle - the acute angle the resultant makes with the x-axis • Calculate based on the quadrant*
*Calculating θ • When calculating the angle, • 1) Use the absolute values of the components to calculate • 2) Compute C using inverse tangent • 3) Compute from based on the quadrant. • Quadrant I: = • Quadrant II: = 180 o - ; • Quadrant III: = 180 o + • Quadrant IV: = 360 o -
(x, y) to (R, ) ACT • Express the vector in (R, ) notation (magnitude and direction) A = (12 cm, -16 cm) A = (20 cm, 307 o)
Vector Addition by Components • Resolve the vectors into x and y components. • Add the x-components together. • Add the y-components together. • Use the method shown previously to convert the resultant from (x, y) notation to (R, ) notation
Practice Problem Given A = (20 m, 40 o) and B = (30 m, 100 o), find the vector sum A + B. A = (15. 32 m, 12. 86 m) B = (-5. 21 m, 29. 54 m) A + B = (10. 11 m, 42. 40 m) A + B = (43. 6 m, 76. 6 o)
Unit Vectors: Notation • Vector A can be expressed in several ways • Magnitude & Direction (A, ) • Rectangular Components (Ax , AY)
- Vectors and scalars in physics
- 5 meters scalar or vector
- Difference between scalar and vector quantity
- Entropy is scalar or vector
- Vectors form 3
- Scalar quantity and vector quantity
- What is a vector quantity
- Scalar quantity and vector quantity
- Multiplying or dividing vectors by scalars results in:
- Magnetic field intensity is scalar or vector
- Which of these expresses a vector quantity
- Quantity y varies inversely as quantity x.
- Scalar versus vector quantities
- Scalar and vector quantity difference
- Extension of scalars
- Vector quantity
- Momentum is a vector quantity
- Momentum is a vector quantity
- A force is a vector quantity because it has both
- Centripetal acceleration is scalar or vector