PHYSICS 231 INTRODUCTORY PHYSICS I pa.msu/courses/phy231

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PHYSICS 231 INTRODUCTORY PHYSICS I www.pa.msu.edu/courses/phy231. Scott Pratt [email protected] (517) 355-9200, ext. 2016 Office Hours: Monday, 9-10:30 AM in 1248 BPS. Course Information. http://www.pa.msu.edu/courses/phy231. Succeeding in Physics 231. Do your homework (yourself)!

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PHYSICS 231INTRODUCTORY PHYSICS Iwww.pa.msu.edu/courses/phy231

Scott Pratt

[email protected]

(517) 355-9200, ext. 2016

Office Hours: Monday, 9-10:30 AM in 1248 BPS

Course Information

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

Succeeding in Physics 231
• Use the help room (1248 BPS) !
• Make sure you understand both “why” and “why not”
• 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…
Dimensional Analysis

Dimensions & units can be treated algebraically.

Dimensional Analysis

Checking equations with dimensional analysis:

(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:

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

Example 1.2

Consider the equation:

Where m and M are masses, r is a radius andv 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?

Yes

Is this equation dimensionally valid?

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

The above expression yields:

40.11 m

4011 cm

A or B

Impossible to evaluate (dimensionally invalid)

Example 1.4b

The above expression yields:

4.5 m kg

4.5 g km

A or B

Impossible to evaluate (dimensionally invalid)

Example 1.4b

The above expression yields:

-1.5 m

-1.5 kg m2

-1.5 kg

Impossible to evaluate (dimensionally invalid)