PHYSICS 231 INTRODUCTORY PHYSICS I www pa msu edu courses phy231 Scott Pratt prattsc msu edu 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 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 Syst me Internationale Dimension Length Mass Time SI mks Unit Definition meters m Distance traveled by light in 1 299 792 458 s kilogram kg Mass of a specific platinum iridium allow cylinder kept by Intl Bureau of Weights and Measures at S vres France seconds s 9 192 631 700 oscillations of cesium atom Standard Kilogram at S vres Dimensional Analysis Dimensions units can be treated algebraically Variable from Eq dimension x m t v xfxi t a vf vi t L M T L T L T2 Dimensional Analysis Checking equations with dimensional analysis 1 2 x f xi vi t at 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 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 2gt2 x Yes Is this equation dimensionally valid vt x 1 mgt2 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 m 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 0kg 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
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