PHYSICS 231INTRODUCTORY PHYSICS I

www.pa.msu.edu/courses/phy231

Scott Prattprattsc@msu.edu

(517) 355-9200, ext. 2016Office Hours:

Monday, 9-10:30 AM in 1248 BPS

Course Information

http://www.pa.msu.edu/courses/phy231

Succeeding in Physics 231

1) Do your homework (yourself)!2) Use the help room (1248 BPS) ! 3) Make sure you understand both “why” and

“why not”4) Interrupt the lecturer!

General Physics

• First Semester (Phy 231)• Mechanics• Thermodynamics• Simple harmonic motion• Waves

Second Semester (Phy 232)• Electromagnetism• Relativity• Modern Physics • (Quantum Mechanics, …,

etc.)

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 platinum-iridium 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:

L (L/T)T=L

(L/T2)T2=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 ) are dimensionless

x f −xi =vit+12at2

Example 1.1

Check the equation for dimensional consistency:

2

2

2

)/(1mc

cv

mcmgh −

−=

Here, m is a mass, g is an acceleration,c is a velocity, h is a length

Example 1.2

L3/(MT2)

Consider the equation:

Where m and M are masses, r is a radius andv is a velocity.What are the dimensions of G ?

mv2

r=G

Mmr2

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?

Yes

Is this equation dimensionally valid?

No

x =(4 / 3)ut

1−(2gt2 / x)

x =vt

1−mgt2

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, m, nm

Example 1.4a

The above expression yields:

40m +11cm=?

a) 40.11 mb) 4011 cmc) A or Bd) Impossible to evaluate (dimensionally invalid)

Example 1.4b

The above expression yields:

1.5m ⋅3.0kg=?

a) 4.5 m kgb) 4.5 g kmc) A or Bd) Impossible to evaluate (dimensionally invalid)

Example 1.4b

The above expression yields:

1.5m-3.0kgm/s=?

a) -1.5 mb) -1.5 kg m2

c) -1.5 kgd) Impossible to evaluate (dimensionally invalid)