Vectors in Physics
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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 5x + 2ŷ 5x̄ < 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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