All Flashcards
What is the key difference between scalars and vectors?
Scalars have only magnitude, while vectors have both magnitude and direction.
Compare distance and displacement.
Distance: Scalar, total path length. Displacement: Vector, change in position from start to end.
Compare speed and velocity.
Speed: Scalar, rate of motion. Velocity: Vector, rate of motion with direction.
Differentiate between mass and weight.
Mass: Scalar, amount of matter in an object. Weight: Vector, force of gravity on an object.
Compare using vector notation in 1D vs 2D.
1D: +/- signs indicate direction. 2D: Use components or magnitude and angle.
What is the difference between distance and displacement?
Distance: Total path length traveled. Displacement: Change in position from the starting point, including direction.
What is the difference between speed and velocity?
Speed: How fast an object is moving (scalar). Velocity: How fast and in what direction an object is moving (vector).
Compare scalar and vector addition.
Scalar addition: Simple arithmetic. Vector addition: Requires considering both magnitude and direction, often using components.
How do scalars and vectors differ in mathematical operations?
Scalars: Obey standard algebraic rules. Vectors: Require special rules (e.g., vector addition, dot product, cross product).
Contrast the use of + and - signs for scalars vs. vectors in 1D.
Scalars: + and - indicate positive or negative values. Vectors: + and - indicate direction along a line.
What is the effect of adding vectors without considering direction?
Incorrect results in physics calculations, especially when analyzing motion or forces.
What is the effect of using unit vectors in vector algebra?
Simplifies calculations and allows for easy conversion between different notations.
What is the effect of applying a force at an angle?
The force must be resolved into components to analyze its effect on motion in different directions.
What is the effect of a changing velocity vector?
It results in acceleration, which can change the object's speed, direction, or both.