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## AS Physics: Scalar & Vector QuantitiesA scalar has magnitude only. A vector has magnitude and direction. Remember that S.I. units must be included for all quantities to define a magnitude. Example scalars: distance, speed, work done, energy, power, time, mass Example vectors: displacement, velocity, acceleration, momentum, force, impulse ## Vector RulesVectors are represented by arrows, the lengths of which indicate relative magnitudes. For example, the vector below has a size of 3 cm. Its direction is clearly indicated as well:
## AddingThe sum of vectors A and B (below) is R (the resultant):
Drawn to scale, we simply join arrows one after the other. The resultant is the vector represented by the arrow that goes from the starting point to the end point. ## SubtractingIn vector terms, there isn't really such a thing as "subtracting" one vector from another. It's easier to think of it as adding a negative vector (i.e. the reverse of the vector being subtracted).
e.g. A - B = R can be written: A + -B = R.
## Perpendicular VectorsThe resultant, R, of two perpendicular vectors, X and Y, is given by Pythagoras‘s Theorem: R² = X² + Y²
## Resolving VectorsPerpendicular components of a vector are two vectors at right angles to each other that add up to give the original vector. This can be very useful indeed! Remember your basic trigonometry: sin q = opposite/hypotenuse
[Click for a trigonometry refresher!] For example, if X and Y are the horizontal and vertical components of R, we can find X and Y if we know another angle, say
Note that the angle between X and Y must be set at 90° so that the components are In this case: opposite represents X, adjacent represents Y and the hypotenuse represents R From the sine and cosine relations: vertical component, Y = R Perpendicular components of vectors act |
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