AP PHYSICS B
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Course Information
http://www.lodiscience.com
Succeeding in AP Physics
1) Do your homework (yourself)!
2) Get help A.S.A.P. when you feel lost!
3) Make sure you understand both “why” and “why
not”
4) Interrupt the lecturer!
5) Study, Study, Practice, Practice, Study and
Practice some more, Then Study so you can
practice!
Mechanics
• Half the course
• Quantified largely by Galileo
• Problems involve:
velocity, acceleration, mass, momentum, energy,
torque, angular momentum, moment of inertia…
UNITS (Systéme Internationale)
Dimension
SI (mks) Unit
Definition
Length
meters (m)
Distance traveled by light in
1/(299,792,458) s
Mass
kilogram (kg)
Mass of a specific platinumiridium allow cylinder kept by
Intl. Bureau of Weights and
Measures at Sèvres, France
Time
seconds (s)
9,192,631,700 oscillations of
cesium atom
Standard Kilogram
at Sèvres
Dimensional Analysis
Dimensions & units can be treated algebraically.
Variable from Eq.
x
m
t
v=(xf-xi)/t
a=(vf-vi)/t
dimension
L
M
T
L/T
L/T2
Dimensional Analysis
Checking equations with dimensional analysis:
1
x f  xi  vi t  at 2
2
(L/T2)T2=L
L
(L/T)T=L
• Each term must have same dimension
• Two variables can not be added if dimensions
are different
• Multiplying variables is always fine
• Numbers (e.g. 1/2 or p) are dimensionless
Example 1.1
Check the equation for dimensional consistency:
2
mc
2
mgh 

mc
2
1  (v / c )
Here, m is a mass, g is an acceleration,
c is a velocity, h is a length
Example 1.2
Consider the equation:
v2
Mm
m G 2
r
r
Where m and M are masses, r is a radius and
v is a velocity.
What are the dimensions of G ?
L3/(MT2)
Example 1.3
Given “x” has dimensions of distance, “u” has
dimensions of velocity, “m” has dimensions of
mass and “g” has dimensions of acceleration.
Is this equation dimensionally valid?
(4 / 3)ut
x
1  (2gt 2 / x)
Yes
Is this equation dimensionally valid?
vt
x
1  mgt 2
No
Units vs. Dimensions
Dimensions: L, T, M, L/T …
Units: m, mm, cm, kg, g, mg, s, hr, years …
When equation is all algebra: check dimensions
When numbers are inserted: check units
Units obey same rules as dimensions:
Never add terms with different units
• Angles are dimensionless but have units
(degrees or radians)
• In physics sin(Y) or cos(Y) never occur unless Y
is dimensionless
•
•
•
•
•
Example 1.3
Grandma traveled 27 minutes at 44 m/s.
How many miles did Grandma travel?
44.3 miles
Prefixes
In addition to mks units,
standard prefixes can be used,
e.g., cm, mm, mm, nm
Example 1.4a
40 m  11cm  ?
The above expression yields:
a)
b)
c)
d)
40.11 m
4011 cm
A or B
Impossible to evaluate (dimensionally invalid)
Example 1.4b
1.5 m  3.0 kg  ?
The above expression yields:
a)
b)
c)
d)
4.5 m kg
4.5 g km
A or B
Impossible to evaluate (dimensionally invalid)
Example 1.4b
1.5 m-3.0 kg m/s  ?
The above expression yields:
a)
b)
c)
d)
-1.5 m
-1.5 kg m2
-1.5 kg
Impossible to evaluate (dimensionally invalid)