1 / 10

Unit Vectors

Unit Vectors. Old school. Consider vector B, which is expressed as B and θ where B is the magnitude and θ is the direction We know that the vector has components in the x and y axis (every vector does) B x and B y We can find these components using trig functions and pythag theorem.

frederick-corbin
Télécharger la présentation

Unit Vectors

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. Unit Vectors

  2. Old school • Consider vector B, which is expressed as B and θ where B is the magnitude and θ is the direction • We know that the vector has components in the x and y axis (every vector does) Bx and By • We can find these components using trig functions and pythag theorem

  3. We always MUST consider the x and y components of a vector to do any type of physics or math problems

  4. New School • Vectors can also be expressed in terms of unit vectors • A unit vector is a dimensionless vector having a magnitude of exactly 1 • The unit vector is only used to specify a given direction • i, j, k are used to represent unit vectors pointing in the direction of the positive x, y, z directions

  5. If we go back to vector B, now we can express it as B at θ = Bxi + Byj since Bx is in the i direction and By is in the j direction So any position vector R can be written as R = Rxi + Ryj (+ Rzk) Ex. If R = 15 m @ 35o , it can be broken into x=12.29 m and y=8.6 m so… R = 12.29 i + 8.6 j m

  6. Adding vectors in unit vector form becomes very easy A + B, where A = Axi + Ayj , B = Bxi + Byj So if A + B = C, then C = (Ax + Bx) i + (Ay + By) j And once we have C, then we can still find it’s polar coordinates, or magnitude and direction (pythag & trig)

  7. Sometimes we will do 3 dimensional problems. You can actually still use pythag theorem to find the resultant magnitude, but never anything with angles (at least for us) • You can add (we saw this), subtract (add opposite), and multiply unit vectors, just like before ex. Find 5A where A = Ax i + Ay j 5A = 5Ax i + 5Ay j

  8. Find the sum of two vectors a) in unit vector notation and b) polar coordinates if A = 2i + 2j and B = 2i – 4j

  9. A particle undergoes three consecutive displacements: d1 = 15i + 30j + 12k cm d2 = 23i – 14j – 5k cm d3 = -13i + 15j cm Find the resultant magnitude of this displacement.

More Related