Physics 121
FALL SEMESTER 2016

INSTRUCTOR: Dr. Sharma

msharma102@yahoo.com

Chapter 3: Kinematics in Two Dimensions; Vectors

Addition of Vectors

• Resultant Vector (): Represents the sum of different vectors

• The magnitude of resultant vector is always smaller than the sum of the magnitudes of the separate vectors (that are not in the same line)

+ ...

1. Graphically:

• Tail-To-Tip Method: A graphical method of displaying the sum of separate vectors.

•  Step 1: The tail of the second vector is placed on the tip of the first vector.

•  Step 2: The resultant vector is represented as the arrow drawn from the tip of the first vector to the tail of the second vector.

 +       

• Negative Vector: A vector similar in magnitude and opposite in direction, to its positive vector.

2. By Components:

• Vector Components: The separate vectors   of the vector , which are perpendicular to the Y and X axis subsequently.

• Figuring: The magnitudes of the components with trigonometry:

∴  

∴  

• Figuring: The angle that the vector D makes with the positive x-axis:

∵

∴

• Figuring: The magnitude of the resultant vector from the sum of vectors:

        Pythagorean Theorem ( )

∴             

∴

• If we wanted to add two or more vectors:

• Step 1: we resolve each vector to its x and y components

 ,

• Step 2: we figure out the sum of the x components

  ,  

• Step3: We figure out the magnitude of the resultant vector