Lect04 - Physics 112: Lecture 4 Todays Agenda More on...

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Physics 112: Lecture 4 Today’s Agenda • More on Vectors • Motion in 2D/3D
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Vector Subtraction How to define A - B ? Define the difference as the vector sum of A and -B : A - B = A + ( -B ) Connect the tail of - B with the head of A A B A -B A -B -B C = A - B
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Vector Algebra Vectors obey these rules:
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A short problem: A C B Vector C = which of the following? (1) A + B (2) B - A (3) A - B (4) other T
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Vector Components • Often easier to break vectors into components along reference directions (less trig) • E.g. in 2 dimensions: x y x
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Products of Vectors • Scalar product (“dot product”) – Will use this later, e.g. to describe work done by a force • Vector product (“cross product”) – Will need this later for torque and angular momentum
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Scalar product A B • Defined as the magnitude of A multiplied by the component of B parallel to A • Result is not a vector! r A r B A B cos φ B φ A B cos φ
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Components of scalar product Scalar product in terms of the components? In 2D: A B = (Axi+Ayj) (Bxi+Byj) =Axi Bxi +Axi Byj + Ayj Bxi + Ayj Byj i i=1, i j=0 = AxBx + AyBy i.e. the scalar product of two vectors is just the sum of the product of the components!
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Lect04 - Physics 112: Lecture 4 Todays Agenda More on...

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