Scalars and Vectors

Understanding Scalars and Vectors

• Scalar quantities have magnitude (size) but don’t have direction. They are the simplest form of quantities that just have a size.
• Examples of scalar quantities include speed, distance, mass, temperature, and energy.
• Vector quantities have both magnitude (size) and direction. Whenever a quantity requires both direction and magnitude for its complete representation, it is defined as vector.
• Examples of vector quantities include velocity, displacement, force, and momentum.

Representing Vectors Graphically

• Vectors can be represented graphically as arrows. The length represents the magnitude and the arrow shows the direction.
• The starting point of the vector is known as the tail and the end point (where the arrow is) is known as the head.
• To add vectors graphically, place the tail of the second vector to the head of the first one, the resultant vector is the vector drawn from the tail of the first vector to the head of the second vector.

Differences Between Distance and Displacement

• Distance is a scalar quantity. It is the measurement of the actual path travelled by an object, regardless of the direction.
• Displacement is a vector quantity. It is a measurement from the initial position to the final position of the object. It is independent of the path taken.

Differences Between Speed and Velocity

• Speed is a scalar quantity that refers to “how fast an object is moving”.
• Velocity is a vector quantity that refers to “the rate at which an object changes its position”; in other words, velocity is speed in a given direction.
• Therefore, speed only has magnitude, while velocity has both magnitude and direction.

How Forces Affect Motion

• A single force acting on an object may cause it to change speed, change direction, or change both its speed and direction. Thus, a force is a vector quantity.
• Forces are measured in Newton (N), and the force’s magnitude and direction determine how it affects an object’s motion.

Newton’s Laws of Motion

• Newton’s first law (also known as the Law of Inertia) states that an object at rest will stay at rest and an object in motion will stay in motion unless acted upon by a net external force.
• Newton’s second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. In equation form: F = ma, where F is the force, m is the mass, and a is acceleration.
• Newton’s third law states that for every action, there is an equal and opposite reaction.