Phys 1111: Vectors and scalars - Practice Flashcards

Question-and-answer flashcards covering scalar vs vector concepts, unit vectors, vector specification methods, 2D vector components, magnitude, direction, and the position vector.

What is a scalar?

A quantity with only magnitude and no direction.

What is a vector?

A quantity with both magnitude and direction; typically represented with an arrow.

What are unit vectors and what do they represent?

Dimensionless vectors of unit length along a coordinate axis used to indicate direction (e.g., x-hat and y-hat).

What are the two common ways to specify vector quantities?

1) Components along coordinate axes (Ax, Ay). 2) Magnitude and direction (|A| and θ).

How is a two-dimensional vector written in component form?

A = Ax x-hat + Ay y-hat.

How do you find a vector's components from its magnitude A and direction angle θ relative to the x-axis?

Ax = A cos θ, Ay = A sin θ.

How do you compute a vector's magnitude from its components Ax and Ay?

|A| = sqrt(Ax^2 + Ay^2).

How do you compute a vector's direction angle θ from its components Ax and Ay?

θ = arctan(Ay / Ax) with quadrant considerations.

What is the relation between components and magnitude/angle when using Ax = A cos θ and Ay = A sin θ?

The x and y components are given by Ax = A cos θ and Ay = A sin θ.

What is the 2D position vector r?

r points from the origin to (x, y); r = x x-hat + y y-hat (or r = (x, y)).

What are the x-hat and y-hat unit vectors?

x-hat is the unit vector in the positive x direction; y-hat is the unit vector in the positive y direction; both are dimensionless and indicate direction.

How do the signs of a vector's components relate to its quadrant?

The signs of Ax and Ay indicate the quadrant the vector lies in (e.g., both positive in QI, Ax negative Ay positive in QII, etc.).

What is the 'lazy method' for determining where sine and cosine go when expressing components?

Use limiting cases where the angle is 0° or 90° to decide which component uses sine or cosine.

What is a 1-D vector and how are directions indicated?

In one dimension, there are two directions; a positive or negative sign on the magnitude indicates the direction relative to a predefined positive direction.

How is the vector magnitude related to its components and angle?

|A| = sqrt(Ax^2 + Ay^2); θ = arctan(Ay/Ax) (with quadrant considerations).