1 / 15

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.

babu
Download Presentation

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

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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 !

More Related