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# 376 Class Note for PHYS 211 at PSU

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This 24 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Pennsylvania State University taught by a professor in Fall. Since its upload, it has received 23 views.

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Date Created: 02/06/15

Chapter 3 Vectors Physics deals with many quantities that have both y r w r 8 I a 15 S IVECTORS X 39Eg Displacement Velocity Acceleration Force Torque x and y components of motion are independent LINEARITY Campanets vX v cos 6 vy vsin6 17 vxvy vx fvy Definitions l SCALAR provides information about how large a measurement is o Gives one item of information magnitude temperatureT l VECTOR provides information about how large a measurement is and the direction of the measurement o Ordered pair numbers required xy 739 9 4 zay ijwwy m2 awnPW LI 7 w 0 MT quot c 39 r a i D 5T quotgtf 3 gt quotW qo f 7 x ij an m M mum alumnae am am Mung D o Ordered pair numbers 6 y 1quot 9 Vector Components L1 VECTOR ALGEBRA I Scalar multiplication I Vectors are added or subtracted according to the rules for ordered pairs l axabxbl coordinates See blackboard c7 away 2 42 15 b 13 bwby 16 29 Unit vectors have magnitude 1 and are unitless they only give the direction VECTOR NOTATION 9 Components for a vector may be expressed in unit vector notation o i is a unit vector in the X direction o is a unit vector in the y direction 0 k is a unit vector in the z direction 9 Bold type or an arrow above the symbol denotes a vector eg A or A O The magnitude of the above vector is designated A s Q g g h D Vectors are added or subtracted according to the rules for ordered pairs u axaJ bxbycxcc00rdinates Rule for graphical addition is implied Displacement Vector now in 2D IDisplacement IThree different paths give the same displacement Addition of displacement vectors a b ADDITIONAL VECTOR PROPERTIES 9A vector can be moved in a diagram so long as the magnitude and direction is unchanged 9 Vectors may be expressed as ordered numbers polar form or in unit vector form 9 Vector subtraction may be accomplished by multiplying the subtracted vector by 1 and using the technique for adding Note he ad 0 all arrangement for addition i a 11r II Ant Example if 1 F4 Homr d M 82 m V Home J M Vector Multiplication I Vectors can be multiplied in two ways 9 A dot product of two vectors results in a gt scalar c 5219 o A cross product esults in another vector I Vectors are NEVER divided Multiplication of two vectors resulting in a scalar Example f Em f311thgamut EXAMPLE 2 What is the dot product of 5053nj 20 155 21 I3 The VECTOR PRODUCT or CROSS PRODUCT I Vector multiplication yielding another vector 5 I Yields a vector which has a direction determined by the right hand rule I Yields a vector perpendicular to the plane containing the other two vectors I The cross product DOES NOT commute 7 797 A W x3977 2quotquotquot l 4 l I My 5 1 I39m K O xx 739 y3 Uquot 91 quot HH 1 1 J a r 70425 4 A s X ngwiyv kmi Myquot 15 44 k DIRECTION OF THE CROSS PRODUCT a 39 I Advance Righ hand rule ll wmuwh Unit Vector Cross Products I Using the de nition of cross product and righthand rule A F m 1394 M 2 N F L44 v 444 V s m Calculate the cross product of 21 500m 300m I 200m1550 Projectile Motion I Classic 2D problem Eqs Of Motion

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