scalar

Meaning: A scalar is a physical quantity fully specified by a number and a unit. A vector needs a magnitude and a direction. Common scalars are distance, speed, time, mass, temperature, density, pressure, energy, work, power and electric potential. Scalars combine by ordinary arithmetic, while vectors combine by components or head-to-tail addition. Multiplying a vector by a scalar changes its length, and reverses its direction if the scalar is negative. The dot product of two vectors is a scalar.

Equation: W = Fd cosθ, where W is work (J), F is the force magnitude (N), d is the displacement magnitude (m), and θ is the angle between the force and the displacement. Work is a scalar even though force and displacement are vectors.

On the MCAT: Questions ask you to sort quantities into scalar or vector, especially distance versus displacement and speed versus velocity. A typical case is a runner who completes a full lap: distance and average speed are nonzero, but displacement and average velocity are zero. Energy methods are often easier than force methods because scalars add with no angles.

Common confusion: A negative sign does not make a quantity a vector. Work, charge and potential energy are scalars that can be negative, and the sign carries meaning other than direction in space. Pressure is also a scalar, even though the force it produces on a surface is a vector.