phys1441-spring08-012308-post

phys1441-spring08-012308-post - PHYS 1441 Section 002...

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Wednesday, Jan. 23, 2008 PHYS 1441-002, Spring 2008 Dr. Jaehoon Yu 1 PHYS 1441 – Section 002 Lecture #3 Wednesday, Jan. 23, 2008 Dr. Jae hoon Yu Dimensional Analysis Trigonometry reminder Coordinate system, vector and scalars One Dimensional Motion: Average Velocity; Acceleration; Motion under constant acceleration; Free Fall
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Wednesday, Jan. 23, 2008 PHYS 1441-002, Spring 2008 Dr. Jaehoon Yu 2 Dimension and Dimensional Analysis • An extremely useful concept in solving physical problems • Good to write physical laws in mathematical expressions • No matter what units are used the base quantities are the same – Length (distance) is length whether meter or inch is used to express the size: Usually denoted as [L] – The same is true for Mass ([M]) and Time ([T]) – One can say “Dimension of Length, Mass or Time” – Dimensions are used as algebraic quantities: Can perform two algebraic operations; multiplication or division
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Wednesday, Jan. 23, 2008 PHYS 1441-002, Spring 2008 Dr. Jaehoon Yu 3 Dimension and Dimensional Analysis • One can use dimensions only to check the validity of one’s expression: Dimensional analysis – Eg: Speed [v] = [L]/[T]=[L][T -1 ] •Distance (L) traveled by a car running at the speed V in time T •L = V*T = [L/T]*[T]=[L] • More general expression of dimensional analysis is using exponents: eg. [v]=[L n T m ] =[L]{T -1 ] where n = 1 and m = -1
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Wednesday, Jan. 23, 2008 PHYS 1441-002, Spring 2008 Dr. Jaehoon Yu 4 Examples Show that the expression [v] = [at] is dimensionally correct • Speed: [v] =L/T • Acceleration: [a] =L/T 2 • Thus, [at] = (L/T 2 )xT=LT (-2+1) =LT -1 =L/T= [v] 2 m =− m n v kr a = Dimensionless constant Length Speed 12 LT = r v v kr a 2 2 1 = = rv a nm + = •Suppose the acceleration a of a circularly moving particle with speed v and radius r is proportional to r n and v m . What are n and m ?
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This note was uploaded on 10/21/2009 for the course PHYS phys1441 taught by Professor Dr.jhaehoonyou during the Spring '08 term at UT Arlington.

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phys1441-spring08-012308-post - PHYS 1441 Section 002...

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