Lecture 2

Lecture 2 - Announcements There are labs starting already...

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There are labs starting already this week. Lab syllabus will be handed to you on your first lab. Now it is available online as well. Physics 220 Help center is in room 11A Lecture 2: January 12, 2011 Purdue University, Physics 220 1 Announcements
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Trigonometry Generally will use right triangles Pythagorean Theorem r 2 = x 2 + y 2 Trig functions (r = hypotenuse) sin θ = y / r cos θ = x / r tan θ = y / x Trigonometric identities sin ² θ + cos ² θ = 1 Other identities are given in appendix B and the back cover To find an angle, you need to use the inverse of a trig function If sin θ = y/r then = sin -1 (y/r)= ascsin(y/r) Angles in a right triangle add up to 90° α + β = 90° Complementary angles sin α = cos β Lecture 2: January 12, 2011 2 Purdue University, Physics 220
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Vectors vs. Scalars • A scalar is a quantity that requires only a magnitude (with unit) time [s], mass [kg]. • A vector is a quantity that requires a magnitude and a direction (is represented by arrows) displacement [m], force [N], velocity [m/s], acceleration [m/s 2 ]. Lecture 2: January 12, 2011 3 Purdue University, Physics 220
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Vector Representation The length of the arrow indicates the magnitude of the vector The direction of the arrow indicates the direction of the vector with respect to a given coordinate system Vectors are written with an arrow over a boldface letter Numerous mathematical operations are defined for vectors: e.g. addition; subtraction; multiplication by constant, dot product, cross product. Lecture 2: January 12, 2011 4 Purdue University, Physics 220
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Vector addition Draw the first vector Draw the second vector starting at the tip of the first vector Continue to draw vectors “tip-to-tail” The sum is drawn from the tail of the first vector to the tip of the last vector Lecture 2: January 12, 2011 5 Purdue University, Physics 220
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Adding Vectors Using Components • To add the vectors, add their components C x = A x + B x C y = A y + B y • Then the magnitude and direction of C can be determined A x = A cos θ ; A y = A sin θ Lecture 2: January 12, 2011 6 Purdue University, Physics 220
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Lecture 2: January 12, 2011 Purdue University, Physics 220 7 + x - x 0 The variables are time and position t = t i start of observations at a point x i t = t f end of the observations at a point x f Δ x = x f – x i ; Δ t = t f – t i ; All quantities except time are vectors; the vector “nature” is
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Lecture 2 - Announcements There are labs starting already...

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