9702 · 1.4
Scalars and vectors flashcards
Revision flashcards for Cambridge 9702 Scalars and vectors (syllabus 1.4). Flip, recall, then mark a real past-paper question.
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What is the primary characteristic that defines a scalar quantity?
Its magnitude (size) only.
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Name three common examples of vector quantities.
Displacement, velocity, force, acceleration, momentum, electric field strength (any three).
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How do you determine the magnitude of the resultant vector when adding two vectors that are perpendicular to each other?
Using Pythagoras' theorem: $R = \sqrt{V_x^2 + V_y^2}$.
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If a vector $V$ makes an angle $\theta$ with the horizontal, what is the formula for its horizontal component?
$V_x = V \cos \theta$.
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How does multiplying a vector by a negative scalar affect its magnitude and direction?
Its magnitude changes proportionally, and its direction is reversed.
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Give two examples of scalar quantities.
Distance, speed, mass, time, temperature, energy (any two).
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How can vectors be visually represented?
By an arrow, where its length signifies magnitude and the arrowhead indicates direction.
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What is vector resolution?
Breaking down a single vector into two components that are at right angles to each other.
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What is the formula for the component of vector $V$ *opposite* to an angle $\theta$?
$V_y = V \sin \theta$.
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What is the 'head-to-tail' method used for?
Graphically adding non-perpendicular vectors using scale diagrams.
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How does multiplying a vector by a positive scalar affect it?
Its magnitude changes proportionally, but its direction remains the same.
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What is a 'resultant vector'?
The single vector that has the same effect as two or more vectors combined. It is the vector sum of the individual vectors.
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When adding two non-perpendicular vectors by components, what is the first step?
Resolve each vector into its perpendicular components (e.g., horizontal and vertical components) using trigonometry.
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What is the key difference between speed and velocity?
Speed is a scalar quantity (magnitude only, e.g., 20 m/s), while velocity is a vector quantity (magnitude and direction, e.g., 20 m/s North).
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Is 'work done' a scalar or a vector quantity, and why?
Work done is a scalar quantity. Although it is calculated from two vectors (force and displacement, $W = \mathbf{F} \cdot \mathbf{d}$), the dot product of two vectors results in a scalar.