Vectors and Scalars Chapter 2

Definitions A vector is a quantity that has both direction and magnitude. Examples of vectors include: position, velocity, acceleration, force, and torque. A scalar is a quantity that has only magnitude. Examples of scalars include: mass and moment of inertia.

The length of each arrow (vector) depicts it’s magnitude. The angle of the arrow (vector) to the right horizontal depicts it’s direction.

Adding Two or More Vectors 1. Get the X, Y components of each vector using Sin and Cos. X = r ( cos 𝜃 ) Y = r ( sin 𝜃 ) 2. Add the X components together to get a resultant x component Rx. Rx = Ax + Bx + Cx + … 3. Add the Y components together to get a resultant y component Ry. Ry = Ay + By + Cy + … 4. Get the magnitude of the resultant vector using the Pythagorean formula. 𝑟= 𝑥 2 + 𝑦 2 5. Get the direction of the resultant vector using the inverse tangent function. 𝜃= tan −1 𝑦 𝑥 6. Convert the angle to 0 – 360 measured CCW from the right horizontal.