Measurements & Uncertainties
Units
Newtons & joules
1 newton = 1 kg * m * s-2
Moving the block for a meter:
1 joule = 1 newton * meter = 1 kg * m2 * s-2
Significant Figures
Rules
● Leading 0s - Not significant
● Captive 0s - Significant
● Trailing 0s - Significant only if the . is present
○ Shows the precision
, ● 5.56 - 3 s.f.
● 14.301 - 5 s.f.
● 0.0041 - 2 s.f.
● 0.0100 - 3 s.f.
● Note: for scientific notation, count the sig. figs. in the scientific notation form, not the
full form
Addition/Subtraction AND averages
● Answer should have same # of decimal places as the number with the smallest # of
decimal places
Multiplication/Division
● Answer should have same # of s.f. as the number with the smallest # of s.f.
Uncertainties
● When adding/subtracting, always add the ABSOLUTE uncertainties
○ Ex. 16.0 ± 0.1 + 12.4 ± 0.01
28.4 ± 0.11
● When multiply/dividing, add the PERCENT uncertainties
○ Ex.
○ Note that percent uncertainties should be to 1 sig fig
● When multiplying/dividing with a number with no uncertainty, multiply/divide the
ABSOLUTE uncertainty too
○ It's like adding the same thing x times
● When raising the uncertainty to a power, just multiply the PERCENT uncertainty by
the exponent
○ It's like multiplying the same thing x times
Vectors
● Write direction in square brackets
○ Ex. 50km/h [E]
● When subtracting vectors, just flip the negative one bozo
, ● There are 2 ways of representing direction:
○ [E 50o N]
○ [50o N of E]
● When calculating vectors, separate x & y components
○ Also define your positive directions
Mechanics
Mechanics = Kinematics (motion) + Dynamics (why things move)
Motion
● position (p)
○ A point in relation to another
○ Ex. my house is 5m [E] from me
, ● distance (s)
○ A scalar, the total distance traveled
● displacement (s)
○ The change in position of an object
● Speed
○ A scalar, distance moved by an object in a time period
● Velocity
○ Vector form of speed, includes direction
Position-time graphs
● A position-time graph shows how the position of an object from a point varies over time
Units
Newtons & joules
1 newton = 1 kg * m * s-2
Moving the block for a meter:
1 joule = 1 newton * meter = 1 kg * m2 * s-2
Significant Figures
Rules
● Leading 0s - Not significant
● Captive 0s - Significant
● Trailing 0s - Significant only if the . is present
○ Shows the precision
, ● 5.56 - 3 s.f.
● 14.301 - 5 s.f.
● 0.0041 - 2 s.f.
● 0.0100 - 3 s.f.
● Note: for scientific notation, count the sig. figs. in the scientific notation form, not the
full form
Addition/Subtraction AND averages
● Answer should have same # of decimal places as the number with the smallest # of
decimal places
Multiplication/Division
● Answer should have same # of s.f. as the number with the smallest # of s.f.
Uncertainties
● When adding/subtracting, always add the ABSOLUTE uncertainties
○ Ex. 16.0 ± 0.1 + 12.4 ± 0.01
28.4 ± 0.11
● When multiply/dividing, add the PERCENT uncertainties
○ Ex.
○ Note that percent uncertainties should be to 1 sig fig
● When multiplying/dividing with a number with no uncertainty, multiply/divide the
ABSOLUTE uncertainty too
○ It's like adding the same thing x times
● When raising the uncertainty to a power, just multiply the PERCENT uncertainty by
the exponent
○ It's like multiplying the same thing x times
Vectors
● Write direction in square brackets
○ Ex. 50km/h [E]
● When subtracting vectors, just flip the negative one bozo
, ● There are 2 ways of representing direction:
○ [E 50o N]
○ [50o N of E]
● When calculating vectors, separate x & y components
○ Also define your positive directions
Mechanics
Mechanics = Kinematics (motion) + Dynamics (why things move)
Motion
● position (p)
○ A point in relation to another
○ Ex. my house is 5m [E] from me
, ● distance (s)
○ A scalar, the total distance traveled
● displacement (s)
○ The change in position of an object
● Speed
○ A scalar, distance moved by an object in a time period
● Velocity
○ Vector form of speed, includes direction
Position-time graphs
● A position-time graph shows how the position of an object from a point varies over time
