Mechanics: Scalars
Mechanics: Scalars
Definition of Scalars in Mechanics
- A scalar is a quantity that only has magnitude, or size.
- Scalars are opposite to vectors which have both magnitude and direction.
- Examples of scalar quantities include mass, speed, energy, and temperature.
Interaction with Vectors
- When adding scalar quantities, we simply combine their magnitudes. For instance, if one person has £5 and another has £7, the total amount is £5 + £7 = £12.
- Scalars can be multiplied or divided by each other to result in another scalar. For example, work, which is a scalar, is calculated by multiplying the force applied (a vector quantity) by the distance moved (a scalar quantity).
Operations Involving Scalars
- Two scalars can be added or subtracted from each other if they have the same units.
- A scalar can be multiplied or divided by another scalar regardless of their units.
- Operations involving scalars follow the common rules of basic algebra.
Importance of Units in Scalars
- When dealing with scalar quantities, the unit used is of high importance. The result of any operation performed on scalars is influenced by the units in use.
- For example, if you’re calculating speed (a scalar quantity) and you have measured distance in metres and time in seconds, your result will be in metres per second.
Practical Examples of Scalars in Mechanics
- Real-world examples of scalar quantities include the mass of an object, the temperature of a gas, or the energy required to heat water.
- These quantities do not have a direction, only a magnitude, so are defined as scalars.