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Force is a vector and is a mechanical disturbance or a load, it can

Force is a vector and is a mechanical disturbance or a load, it can deform the object, change its motion, or both (think of kicking a football). (line of action, direction). Length of arrow is proportional to the magnitude if there is more than one force. Summary of vector operations.

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Force is a vector and is a mechanical disturbance or a load, it can

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  1. Force is a vector and is a mechanical disturbance or a load, it can deform the object, change its motion, or both (think of kicking a football) (line of action, direction) Length of arrow is proportional to the magnitude if there is more than one force

  2. Summary of vector operations negative of any vector is a vector of same magnitude pointing in the opposite direction Addition 3 coplanar vectors Tip to tail method C Resultant Parallelogram method, coplanar s is a line onto which A is projected, As is the projection of A onto line s, note That As = A cos 

  3. Resolution of Vectors onto the x and y axis of a 2 D system, the reverse of adding two vectors by parallelogram method The components of the vector A are Ax and Ay and they act In the x and y directions, they Are given by: Ax = A cos  Ay = A sin 

  4. Unit vectors have a magnitude of 1 Note that the book’s vector terminology is such that an underlined variable denotes a vector and if the name is not underlined that is the magnitude of the vector

  5. Unit coordinate vectors The letters i , j , k are commonly used to denote the unit coordinate vectors in the x, y, z directions of a Cartesian coordinate system So a vector like A can be written In terms of these unit vectors and the Components Ax, Ay, Az as A = Ax i + Ay j + Az z

  6. Steps: • First resolve each vector into • its component parts where • for example Ax = A cos  • and Ay = A sin  • 2. Then we can write that • A = Ax i + Ay j • = A cos  i + A sin  j • 3. Magnitude of A is also given • by A = ( Ax2 + Ay2 )1/2 • 4. Likewise for vector B we have • B = B cos  i + B sin  j • 5. C = A + B so we have that • C = (Acos + Bcos) i + • (Asin + Bsin) j • Hence • Cx = (Acos + Bcos) • Cy = (Asin + Bsin) Trig method for adding vectors

  7. 6. C = ( Cx2 + Cy2 )1/2  = tan-1 (Cy / Cx)

  8. Dot or scalar product is defined as the product of the magnitude of two vectors multiplied by the cosine of the angle between them A B = A B cos  Conceptually it is the same as projecting vector B onto the line of action of vector A, ie. Ba = B cos  then multiplying this by the magnitude of A • What is: • i i = ? • i  j = ?

  9. So to take the dot or scalar product of two vectors A and B we proceed as follows below: After recognizing these very important unit coordinate vector identities:

  10. A x B = C, where the vector C has a magnitude equal to the product of the magnitudes of A and B times the sine of the angle , So we can write C = A B sin  Note that vector C has a direction that Is perpendicular to the plane defined By vectors A and B, so in this example C is coming out at us along the z axis Vector or cross

  11. vector Sense is based on the right hand rule

  12. Note a vector !

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