perpendicular
Summary
Perpendicular means at a 90° angle to a line, surface, or vector. The most testable consequence is that a force perpendicular to the displacement does no work (cos 90° = 0), so it can change direction without changing speed.
Detail
Meaning: Perpendicular means at 90° to a line, surface, or vector. Perpendicular components are independent, so a vector can be split into x and y parts and each analyzed separately. A force perpendicular to the displacement does no work, and a force perpendicular to velocity changes direction but not speed.
Equation: W = Fd cosθ, where W is work (J), F is force (N), d is displacement (m), and θ is the angle between F and d; at 90°, cosθ = 0, so W = 0.
On the MCAT: Inclines: the normal force is perpendicular to the surface, and weight splits into mg sinθ parallel and mg cosθ perpendicular to it. Circular motion: centripetal force is perpendicular to velocity, so speed stays constant. Magnetism: F = qvB sinθ is greatest when v is perpendicular to B, and the force is perpendicular to both v and B.
Common confusion: Perpendicular to a surface is not the same as vertical: on a tilted incline the normal force is perpendicular to the incline. Also, a perpendicular force is not zero force; it does no work but still turns the motion.
Sources
- Physics (Giancoli)
- Fundamentals of Physics (Halliday, Resnick, Walker)
- Physics (Cutnell and Johnson)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.