1. Chapter 1: Measurements & Units
Chapter 2: 1D Kinematics
Thursday January 6th
The International system of units (SI)
Prefixes for SI units
Orders of magnitude
Changing units
Length, time and mass standards
Motion in a straight line (1D Kinematics)
Average velocity and average speed
Instantaneous velocity and speed
Acceleration
Reading: pages 1 – 22 in the text book (Chs. 1 & 2)

2. Physics 2048: Reminders Refer to Appendix A in Text Book
First LON-CAPA assignment due Monday
First assignment mainly review (not all covered in lecture)
Very strict deadline of 11:59:59 pm on due date
First Mini-Exam next Thursday (Jan. 13th)
You must attend your first lab next week (M/W)
Refer to Appendix A in Text Book
Trigonometry, Law of cosines, etc….

3. The International System of Units
Système International (SI) d'Unités in French
a.k.a. metric or SI units
Scientists measure quantities through comparisons with standards.
Every measured quantity has an associated unit.
The important thing is to define sensible and practical "units" and "standards" that scientists everywhere can agree upon.
(e.g. Rocket Scientists)
Do an example of the unit of power (watt) in the base units of mass, distance and time.
Electric current (Ampere)
Temperature (Kelvin)
Amount of a substance (mole) - not a mass, simply related to the number of atoms or molecules
luminous intensity (candela)
Click on table to get all seven base units

4. The International System of Units
Système International (SI) d'Unités in French
a.k.a. metric or SI units
Even though there exist an essentially infinite number of different physical quantities, we need no more than seven base units/quantities from which all others can be derived.
In 1971, the 14th General Conference on Weights and Measures picked these seven base quantities for the SI, or metric system.
In Mechanics, we really only need three of these base units (see table)
In Thermodynamics, we need two more Temperature in kelvin (K) Quantity in moles (mol)
Do an example of the unit of power (watt) in the base units of mass, distance and time.
Electric current (Ampere)
Temperature (Kelvin)
Amount of a substance (mole) - not a mass, simply related to the number of atoms or molecules
luminous intensity (candela)
Click on table to get all seven base units

5. Prefixes for SI Units Scientific notation:
m = 3.56 × 109 m
s = 4.92 × 10-7 s
On LON-CAPA = 4.92*10^-7 s
On your calculator (also LON-CAPA):
4.92 × 10-7 = 4.92 E-7 or
Prefixes (also works in LON-CAPA):
5 × 109 watts = 5 gigawatts = 1 GW
2 × 10-9 s = 2 nanoseconds = 2 ns

6. Orders of magnitude

7. Changing units 1 minute = 60 seconds
Chain-link conversion - an example:
1 minute = 60 seconds
Note: this does not imply 60 = 1, or 1/60 = 1!

8. Conversion Factors
Etc., etc., etc…….
Resources at your fingertips…

9. Quiz #1
Which of the following have been used as the standard for the unit of length corresponding to 1 meter?
a) One ten millionth of the distance from the North pole to the equator.
b) The distance between two fine lines engraved near the ends of a platinum-iridium bar.
c) 1 650  wavelengths of a particular orange-red light emitted by atoms of krypton-86 (86Kr).
d) The length of the path traveled by light in a vacuum during a time interval of 1/299 792 458 of a second.

10. Length 1792: French established a new system of weights and measures
1 m = distance from N. pole to equator ten-million
Then, in the 1870s:
1 m = distance between fine lines on Pt-Ir bar
Accurate copies sent around the world
Then, in 1960:
1 m = × wavelength 86Kr (orange)
1983 until now (strict definition):
1 m = distance light travels in 1/( ) sec

11. Time United States Naval Observatory
Some standards used through the ages:
Length of the day
Period of vibration of a quartz crystal
Now we use atomic clocks
1 second equivalent to oscillations of the light emitted by a cesium-133 atom (133Cs) at a specified wavelength (adopted 1967)
United States Naval Observatory

12. Mass Kilogram standard is a Pt-Ir cylinder in Paris
Accurate copies have been sent around the world; the US version is housed in a vault at NIST
A second mass standard:
The 12C atom has been assigned a mass of 12 atomic mass units (u)
1 u = × Kg
The masses of all other atoms are determined relative to 12C
Note: we measure "mass" in kilograms. Weight is something completely different, which we measure in Newtons ( kgm/s2)

13. Summary

14. Motion in one-dimension
We will define the position of an object using the variable x, which measures the position of the object relative to some reference point (origin) along a straight line (x-axis).
Positive direction
Negative direction

15. Motion in one-dimension
We will define the position of an object using the variable x, which measures the position of the object relative to some reference point (origin) along a straight line (x-axis).
Positive direction
Negative direction

16. Motion in one-dimension
We will define the position of an object using the variable x, which measures the position of the object relative to some reference point (origin) along a straight line (x-axis).
In general, x will depend on time t.
We shall measure x in meters, and t in seconds, i.e. SI units.
Although we will only consider one-dimensional motion here, we should not forget that x is really a vector. Thus, motion in the +x and -x directions corresponds to motion in opposite directions.
Positive direction
Negative direction

17. Graphing x versus t
x(t)

18. x2 x1 Displacement Displacement Dx: Dx = x2 - x1
final - initial position x2
Like x, Dx is a vector quantity
Its magnitude represents a distance
The sign of Dx specifies direction x1

19. Average velocity
Dx = 4 m - (-10 m) = 14 m
Dt = 5 s - 0 = 5 s

20. Average velocity and speed
Like displacement, vavg is a vector
savg is not a vector - it lacks an algebraic sign
How do vavg and savg differ?
Average speed savg:

22. Instantaneous velocity and speed
Instantaneous speed
= magnitude of v v2 v1
v3 > v1 > v2

23. Acceleration An object is accelerating if its velocity is changing
Average acceleration aavg:
Instantaneous acceleration a:
This is the second derivative of the x vs. t graph
Like x and v, acceleration is a vector
Note: direction of a need not be the same as v

24. Decelerating a a v v
x(t)
Accelerating

25. Decelerating a a v v
v(t)
x(t)
Accelerating

26. Decelerating a a v v
v(t)
a(t)
Accelerating

27. Summarizing Displacement: Dx = x2 - x1 Average velocity:
Average speed:
Instantaneous velocity:
Instantaneous speed: magnitude of v

28. Summarizing Average acceleration: Instantaneous acceleration:
In addition:
SI units for a are m/s2 or m.s-2 (ft/min2 also works)

29. The sensation of acceleration
You will soon learn that, in order to accelerate an object, one must exert a net force on that object.
Thus, when you accelerate, you experience stresses associated with the net force applied to your body.
Therefore, your body is an accelerometer.
When you travel at a constant velocity, be it on a bicycle at 10 ms-1, or a supersonic aircraft at 1500 mph, you are not accelerating. Therefore, you do not feel the sensation of any net force, i.e. your body is not a speedometer.
Acceleration is often expressed in terms of g units, where g (= 9.8 ms-1) is the magnitude of the acceleration of an object falling under gravity close to the earth's surface.

30. Constant acceleration: a special case
For non-calculus derivations, see section 2-4 in text book
To evaluate the constant of integration C, we let v = vo at time t = 0, i.e. vo represents the initial velocity.
Taking the derivative of Eq. 2-7 (vo and a are constants), we recover:

31. Further integration
Note - in general, v depends on t. However, we can substitute v from Eq. 2-17:
To evaluate the constant of integration C', we let x = xo at time t = 0, i.e. xo represents the initial position.

33. Equations of motion for constant acceleration
Equations 2-11 and 2-15 contain 5 quantities: a, t, v, vo and the displacement x - xo.
Both equations contain a, t and vo.
One can easily eliminate either a, t or vo by solving Eqs and 2-15 simultaneously.

34. Free fall acceleration
If one eliminates the effects of air resistance, one finds that all objects accelerate downwards at the same constant rate, regardless of their mass (Galileo).
That rate is called the free-fall acceleration g.
The value of g varies slightly with latitude, but for this course g is taken to be 9.8 ms-2 at the earth's surface.
Thus, the equations of motion in table 2-1 apply to free-fall near the earth's surface.
HRW substitute the coordinate y for x in problems involving free-fall.
It is customary to consider y as increasing in the upward direction. Therefore, the acceleration a due to gravity is in the negative y direction, i.e. a = -g = -9.8 ms-2.