Forces & Motion
Electrons & Photons
AS Physics: Scalar & Vector Quantities
A 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
Vectors 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:
The 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.
In 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.
The resultant, R, of two perpendicular vectors, X and Y, is given by Pythagoras‘s Theorem: R² = X² + Y²
Perpendicular 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 q as shown on the diagram:
Note that the angle between X and Y must be set at 90° so that the components are perpendicular.
In this case: opposite represents X, adjacent represents Y and the hypotenuse represents R
From the sine and cosine relations:
vertical component, Y = Rcosq (since cosq = A/H = Y/R)
Perpendicular components of vectors act independently. For example a horizontal force will cause horizontal not vertical acceleration. Acceleration due to gravity downwards will only change vertical velocity, not horizontal velocity.
|© 2006 A P Harmsworth. All rights reserved. E&OE. Bookmark. Advertise. GCSE revision. Top^^|