Question

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.

Answer 1

Scalar quantity is a physical quantity that has only magnitude but not direction.

Vector quantity is a physical quantity that has both magnitude and direction.

The volume, mass, speed, density, number of moles and angular frequency are the scalar quantities, since they have only one magnitude.

Displacement is defined as,

s → = s 2 − s 1

Here, s → is the displacement.

Displacement is vector quantity, since it has both magnitude and direction.

Velocity is defined as,

v → = s → t

Here, v → is the velocity, t is the time and s → is the displacement.

Since, displacement is vector quantity, so the velocity is also vector quantity.

Acceleration is defined as,

a → = v → t

Here, a → is the acceleration.

Since, the velocity is a vector quantity, so the acceleration is also a vector quantity.

Angular velocity is defined as,

ω → = v → r

Here, ω → is the angular velocity.

Since the velocity is a vector quantity, so the angular velocity is also a vector quantity.

Therefore, the acceleration, velocity, displacement and angular velocity are the vector quantities.