Vectors and Scalars

Vectors and Scalars

Definition

• Scalar quantities only have magnitude (size) and no direction.
• Vector quantities have both magnitude and direction.

Scalar Quantities: Examples

• Distance: The total space travelled by an object. Does not account for direction.
• Speed: The rate at which an object travels through space. Again, it does not consider direction.
• Mass: The amount of matter in an object. Direction does not apply.
• Time: Measurement of the duration. It’s a scalar quantity as it doesn’t include direction.
• Temperature: A measure of the degree of hotness or coldness of a body. It also doesn’t consider direction.

Vector Quantities: Examples

• Displacement: Total distance moved in a particular direction from the starting to the finishing point.
• Velocity: Speed in a particular direction.
• Force: A push or pull on an object. It comprises of both magnitude (how hard it is pushed or pulled) and direction (where it is pushed or pulled).
• Acceleration: The rate at which velocity changes. It includes direction as well.
• Momentum: Mass of an object multiplied by its velocity.

Note: Always remember that while representing vector quantities, the direction is quite important, and it is usually represented with an arrow where the length of the arrow represents magnitude and the direction of the arrow signifies the direction of the quantity.

Adding Vectors

• If two vectors are pointing in the same direction, the resultant vector is the sum of their magnitudes.
• If two vectors act in opposite directions, then their resultant is the difference of their magnitudes.
• For vectors in perpendicular direction, use Pythagoras’ theorem to calculate the resultant vector.

Subtracting Vectors

• To subtract a vector, you flip the vector to be subtracted, and then add.

Remember, studying vectors and scalars is essential to understanding motion because they describe how an object moves, where it goes, how far it travels, and how it responds to forces acting on it.