Question

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

Solution:

Hint: To determine whether a physical quantity is a scalar or a vector, you need to consider whether it has both magnitude and direction.

Step-by-step Solution:

1. Scalar quantities:

• Volume: Scalar quantity because it only has magnitude (e.g., 1 cubic meter).

• Mass: Scalar quantity because it only has magnitude (e.g., 1 kilogram).

• Speed: Scalar quantity because it only has magnitude (e.g., 10 meters per second).

• Density: Scalar quantity because it only has magnitude (e.g., 1000 kilograms per cubic meter).

• Number of moles: Scalar quantity because it only has magnitude (e.g., 1 mole).

2. Vector quantities:

• Velocity: Vector quantity because it has both magnitude and direction (e.g., 10 meters per second to the north).

• Acceleration: Vector quantity because it has both magnitude and direction (e.g., 9.8 meters per second squared down).

• Angular frequency: Vector quantity because it has both magnitude and direction (e.g., 10 radians per second clockwise).

• Displacement: Vector quantity because it has both magnitude and direction (e.g., 10 meters to the north).

• Angular velocity: Vector quantity because it has both magnitude and direction (e.g., 10 radians per second clockwise).

Answer:

Scalar quantities: volume, mass, speed, density, number of moles

Vector quantities: velocity, acceleration, angular frequency, displacement, angular velocity

Note: Some physical quantities can be both scalar and vector, depending on how they are measured. For example, temperature is a scalar quantity, but temperature gradient is a vector quantity. Similarly, work is a scalar quantity, but power is a vector quantity.