This live-action video program is about the word Scalars. The program is designed to reinforce and support a student's comprehension and retention of the word Scalars through use of video footage, photographs, diagrams and colorful, animated graphics and labels.
Viewers will see and hear Scalars used in a variety of contexts providing students with a model for how to appropriately use the word. Related words are also used and reinforced with visuals and text.
A scalar or scalar quantity in physics is a physical quantity that can be described by a single element of a number field such as a real number, often accompanied by units of measurement. A scalar is usually said to be a physical quantity that only has magnitude and no other characteristics. This is in contrast to vectors, tensors, etc. which are described by several numbers that characterize their magnitude, direction, and so on.
The concept of a scalar in physics is essentially the same as in mathematics. Formally, a scalar is unchanged by coordinate system transformations. In classical theories, like Newtonian mechanics, this means that rotations or reflections preserve scalars, while in relativistic theories, Lorentz transformations or space-time translations preserve scalars.
An example of a scalar quantity is temperature: the temperature at a given point is a single number. Velocity, on the other hand, is a vector quantity: velocity in three-dimensional space is specified by three values; in a Cartesian coordinate system the values are the components of speed along each coordinate axis. The associated fields describe the temperature and velocity in each point of some space. Considering the norms of the velocity vectors results in a scalar field of the speeds in each point of the space.
Some examples of scalar quantities in physics are mass, charge, volume, time, speed, and electric potential at a point inside a medium. The distance between two points in three-dimensional space is a scalar, but the direction from one of those points to the other is not, since describing a direction requires two physical quantities such as the angle on the horizontal plane and the angle away from that plane. Force cannot be described using a scalar, since force has both direction and magnitude; however, the magnitude of a force alone can be described with a scalar, for instance the gravitational force acting on a particle is not a scalar, but its magnitude is. The speed of an object is a scalar.
In the theory of relativity, one considers changes of coordinate systems that trade space for time. As a consequence, several physical quantities that are scalars in "classical" (non-relativistic) physics need to be combined with other quantities and treated as four-vectors or tensors. For example, the charge density at a point in a medium, which is a scalar in classical physics, must be combined with the local current density (a 3-vector) to comprise a relativistic 4-vector. Similarly, energy density must be combined with momentum density and pressure into the stress–energy tensor.
Examples of scalar quantities in relativity include electric charge, spacetime interval, and invariant mass.
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