IB PHYSICS HL // Topic 1

kilo

10^3

mega

10^6

giga

10^9

milli

10^-3

micro

10^-6

nano

10^-9

dimensional analysis

Solving the equation to see if units on both sides of the equation match (can only tell if wrong)

systematic error

biases readings in a direction (always bigger/smaller);
causes inaccuracy;
can't be minimized

random error

fluctuations in readings that vary in direction each time;
causes imprecision;
minimized by averaging related trials

uncertainty

analogue: ± 1/2 of smallest division
digital: ± 1 of last digit shown
round to 1 sig fig

accuracy

how close measurement is to true value

precision

how close values are to each other

7 fundamental si units

time (s); length: (m); mass (kg); temp. (k) kelvin; quantity of matter (mol); electric current (A); luminous intensity (cd) candela

Derived Units

units that are combinations of fundamental units. These combinations may or may not have a separate name. (eg. 1 kg m/s2 = 1 N)

absolute uncertainty

just the original uncertainty

fractional (or relative) uncertainty

absolute uncertainty/measurement

percentage uncertainty

fractional uncertainty × 100

significant figures

digits with physical meaning

sig fig rules

1. all non zeros are significant.
2. 0s btwn sig figs are significant.
3. Ending zeros on right side of decimal are significant.

directly proportional

y=kx (positive straight line)

inversely proportional

y=k/x (negative curve)

exponential

y=k^x (positive curve)

scalar

has magnitude

vector

has magnitude + direction

equal vectors

same magnitude and direction

parallel vectors

vectors with same direction

opposite vectors

same magnitude, opposite direction

resultant vector

the vector sum of two or more vectors

adding vectors

tip to tail

subtracting vectors

A-B=A+(-B)

denotating direction

Y(angle)X
N/S(angle)E/W

Component Method

Using the x- and y- directions of motion to determine an overall vector

how to plot graphs

title
axes
scales
data points
best fit line

how can systematic error effect accuracy?

shifts graph horizontally/vertically

how can random error effect precision?

creates noise in data that deviates points from avrg

+/- UNCERTAINTIES

just add absolute uncertainties

×/÷ UNCERTAINTIES

add fractional uncertainties together multiplied by final measurement

how to find best fit line?

1. draw max + min lines that go thru all error bars.
2. calculate max + min slopes and y-intercept.
3. calculate absolute uncertainty with the range divided by 2

how to linearize a graph

arrange the equation with one variable on the left of the equal sign, everything else on the right.
Everything on the left is the vertical axis; your variable on the right is the horizontal axis; everything else is a coefficient that equal the slope.
Example: v^2 = (k/m) x^2
plot v^2 vs. x^2 to create a linear graph; (k/m) equals the slope of the line

Orders of Magnitude

rounding a number to the nearest power of 10
(ex: 275 has an order of magnitude of 10^2)

error bars

creates a zone of uncertainty; shows the uncertainty in measurement for a graph