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

Acceleration: Acceleration is velocity by time. Since velocity is a vector quantity and time is a scalar quantity. But dividing a vector by a scalar gives a vector quantity. Therefore, acceleration is a vector quantity.
Velocity: Velocity is displacement by time. Displacement is a vector quantity and time is a scalar quantity. We know that dividing a vector by a scalar gives us a vector quantity. Therefore, velocity is a vector quantity.
Displacement: Displacement is considered as the minimum distance between the initial and the final point of the object within a given time and is represented visually as an arrow that points from the initial position to the final position.
Angular velocity: It is a vector because it conveys magnitude and direction (for the rotation). It also obeys the regular rules of vector algebra.
So, acceleration, velocity, displacement and angular velocity are vector quantities.
Speed: The rate of change of distance is called speed. It is a scalar quantity.
Mass, volume, density, number of moles, and angular frequency are scalar quantities.