Chapter 4:-

Motion in a plane

(Scalar and Vector Quantity)

PRERNA TANDALE

Introduction

A lot of mathematical quantities are used in Physics to explain the concepts clearly. A few examples of these include force, speed, velocity and work. These quantities are often described as being a scalar or a vector quantity. Scalars and vectors are differentiated depending on their definition. A scalar quantity is defined as the physical quantity that has only magnitude, for example, mass and electric charge. On the other hand, a vector quantity is defined as the physical quantity that has both magnitude as well as direction like force and weight. The other way of differentiating these two quantities is by using a notation. In this article, let us try to learn what is a vector and a scalar quantity.

Scalar and Vector Quantity

Scalar Quantity =

Scalar quantity is defined as the physical quantity with magnitude and no direction.

Some physical quantities can be described just by their numerical value (with their respective units) without directions (they don’t have any direction). The addition of physical quantities follows the simple rules of the algebra. Here, only their magnitudes are added.

Examples of Scalar Quantities

Mass, Speed, Distance, Time, Area, Volume, Density, Temperature

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Vector quantity =

A vector quantity is defined as the physical quantity that has both direction as well as magnitude.

A vector with the value of magnitude equal to one and direction is called unit vector represented by a lowercase alphabet with a “hat” circumflex. That is “û“.

Examples of Vector Quantities

Linear momentum, Acceleration, Displacement, Momentum, Angular, velocity, Force, Electric field, Polarization

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How to Draw a Vector

A vector is drawn as an arrow with a head and a tail. The magnitude of the vector is often described by the length of the arrow. The arrow points in the direction of the vector. See the picture above.

How to Write a Vector

Difference Between Scalar and Vector�

Interesting Facts about Scalars and Vectors

• Unit vectors are vectors with a magnitude of 1. They are used to define direction.
• The credit for inventing vectors is usually given to Irish physicist William Rowan Hamilton.
• Vectors and scalars are important in many fields of math and science.
• Vectors can be defined in two dimensional or three dimensional space.
• Vector graphics are sometimes used in computers because they can be scaled to a larger size without losing any image quality.

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 Is it a scalar or a vector?

1) The football player was running 10 miles an hour towards the end zone.� = This is a vector because it represents a magnitude (10 mph) and a direction (towards the end zone). This vector represents the velocity of the football player.��2) The temperature of the room was 15 degrees Celsius.� = This is a scalar, there is no direction.�

• 3) The volume of that box at the west side of the building is 14 cubic feet.� = This is a scalar. It might be a bit tricky as it gives the location of the box at the west side of the building, but this has nothing to do with the direction of the volume which has a magnitude of 14 cubic feet.��4) The car accelerated north at a rate of 4 meters per second squared.� = This is a vector as it has both direction and magnitude. We also know that acceleration is a vector quantity.

Questions

Q1: Given below is a list of quantities. Categorize each quantity as being

either a vector or a scalar.

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Answer:

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Q3. What is the magnitude of a unit vector?

Answer: The magnitude of a unit vector is unity. A unit vector has no units or dimensions.

Q4. State for each of the following physical quantities, if it is a scalar or a vector.

Volume, Mass, Speed, Velocity, Displacement, Acceleration, Density, Number of Moles, Angular Frequency, Angular Velocity, Displacement

Answer: Scalar: Volume, Mass, Speed, Velocity, Density, Number of Moles, Angular Frequency

Vector: Acceleration, Velocity, Displacement, Angular Velocity.

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Q5. Steve is driving in his car to take care of some errands. The first errand has him driving to a location 2 km East and 6 km North of his starting location. Once he completes that errand, he drives to the second one which is 4 km East and 2 km South of the first errand. What is the magnitude of the vector that describes how far the car has traveled from its starting point, rounded to the nearest km?