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Vectors in Physics

by: Daria

Vectors in Physics 2070

Marketplace > Clemson University > Physics > 2070 > Vectors in Physics
GPA 4.0
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About this Document

These notes cover vectors in physics including adding and subtracting vectors
General Physics 1
Amy Pope
Class Notes
vectors, Physics




Popular in General Physics 1

Popular in Physics

This 2 page Class Notes was uploaded by Daria on Tuesday August 30, 2016. The Class Notes belongs to 2070 at Clemson University taught by Amy Pope in Fall 2016. Since its upload, it has received 7 views. For similar materials see General Physics 1 in Physics at Clemson University.


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Date Created: 08/30/16
Vectors in Physics    Scalars and Vectors  ● Scalar: number with a magnitude  ● Vector: quantity with magnitude and direction  ○ Unit vectors are dimensionless vectors of unit length    5​x                        + 2ŷ   ​5​x̄   <­­­ Resultant vector    ● Equality: A=B if and only if A and B have the same magnitude (length) and direction  (orientation)  ● Negative of a vector   ● Multiplication by a scalar                    Vector Components  ● Signs of vector components  ● Length, angle, and components can be calculated from each other using trigonometry.  opposite y ○ sinθ= hypotenuse r  ○ cosθ=  adjacen=    hypotenuse r ○ tanθ =  adjacent x ● Suppose we are given x and y and need to find r and θ   ○ θ = tan  ( )  x 2 2 ○ r = √ x  + y    ● Or if we are given r and θ , we can find x and y  ○ y = r sinθ   ○ x = rcosθ     Adding and Subtracting Vectors Graphically  ● Adding Vectors:     A ↑ + B→ =  A+B = B+A  ● Subtracting Vectors:     ↑ A ­ B→= ↑A + ­B←= A+­B  ○ The negative of a vector is the same magnitude but opposite direction, so  subtracting a vector is the same as adding a negative vector    Adding and Subtracting Vectors Numerically  ● Adding vectors using components  a. Find the components of each vector to be added  b. Add the x and y components separately  c. Find the resultant vector  ■ Ax + Bx = Rx  Ay + By = Ry  ●    ■ R =  R x+ R y        Magnitude  −1 R y tan  ( R x)  = θ       Direction    Vector Application  ● A: 2.50km SE  B: 4.00km 60   N of E  ● Ax = 2.50cos(­45) = 1.77km     Ay = 2.50sin(­45) = ­1.77km  ● Bx = 4.00cos(60) = 2.00km      By = 4.00sin(60) = 3.46km  ○ Ax + Bx = 3.77km = Rx  ○ Ay + By = 1.69km = Ry  2 2 ■ R = √ (3.77)  +  (1.69)  = 4.13km  ■ tanθ = R x  θ =tan  (  Rx ) = tan  ( 1.6)   θ =24.1   N of E  Ry R y 3.77   Scalars and Vectors  ● Average velocity vector V    = Δr = r(final) −r(i itial) Avg Δt Δt ○ Δ= the change in = final quantity ­ initial quantity  ○ R = position  ● The instantaneous velocity vector is tangent to the path  ● Average acceleration vector is the direction of the change in velocity    Relative Motion  ● The laws of physics which apply when you are at rest on the earth also apply when you  are in any reference frame which is moving at a constant velocity with respect to the  earth. 


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