Class 11 NCERT PHYSICS • Chapter 3: Motion in a Plane • Question 1

QUESTION 1

State, for each of the following physical quantities, if it is a scalar or a vector : volume, mass, speed, acceleration, density, number of moles, velocity, angular frequency, displacement, angular velocity.

SOLUTION

We need to classify the given physical quantities as scalars or vectors based on their magnitude and direction.

Concept: Scalar and Vector

A physical quantity is classified as a scalar if it is fully described by its magnitude alone. It is classified as a vector if it requires both magnitude and direction for a complete description.

Given:

Physical quantities: volume, mass, speed, acceleration, density, number of moles, velocity, angular frequency, displacement, angular velocity.

Solving:

Identify Scalar Quantities

These quantities do not have a spatial direction associated with them.
Volume: A measure of three-dimensional space.
Mass: The amount of matter in an object.
Speed: The magnitude of the rate of change of position.
Density: Mass per unit volume.
Number of moles: A measure of the amount of substance.
Angular frequency: The rate of change of the phase of a waveform, denoted as $\omega$ .

Identify Vector Quantities

These quantities require a direction to be fully defined.
Acceleration: The rate of change of velocity; it points in the direction of the net force.
Velocity: The rate of change of displacement; it includes the direction of motion.
Displacement: The straight-line distance and direction from an initial to a final position.
Angular velocity: A vector quantity representing the rate of rotation around a specific axis.

Answer:

\text{Scalars: volume, mass, speed, density, number of moles, angular frequency; Vectors: acceleration, velocity, displacement, angular velocity}

Motion in a Plane