general physics i, lec 1 by: t.a.eleyan 1 lecture (2)

general physics I, lec 1 By: T.A.Eleyan

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Lecture (2)

general physics I, lec 1 By: T.A.Eleyan

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Scalars and Vectors Scalars have magnitude only. Length, time, mass, speed and volume are examples of scalars.

Vectors have magnitude and direction. The magnitude of   is written |  | Position, displacement, velocity, acceleration and force are examples of vector quantities.

general physics I, lec 1 By: T.A.Eleyan

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Properties of Vectors

Equality of Two Vectors

Two vectors are equal if they have the same magnitude and the same direction

Movement of vectors in a diagram

Any vector can be moved parallel to itself without being affected

general physics I, lec 1 By: T.A.Eleyan

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Negative Vectors

Two vectors are negative if they have the same magnitude but are 180° apart (opposite directions)

Multiplication or division of a vector by a scalar results in a vector for which

)a (only the magnitude changes if the scalar is positive )b (the magnitude changes and the direction

is reversed if the scalar is negative.

general physics I, lec 1 By: T.A.Eleyan

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Adding Vectors

When adding vectors, their directions must be taken into account and units must be the same

First: Graphical Methods

Second: Algebraic Methods

general physics I, lec 1 By: T.A.Eleyan

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Adding Vectors Graphically (Triangle Method)

Continue drawing the vectors “tip-to-tail”

The resultant is drawn from the origin of A to the end of the last vector

Measure the length of R and its angle

general physics I, lec 1 By: T.A.Eleyan

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When you have many vectors, just keep repeating the process until all are included

The resultant is still drawn from the origin of the first vector to the end of the last vector

general physics I, lec 1 By: T.A.Eleyan

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Alternative Graphical Method Parallelogram Method

When you have only two vectors, you may use the Parallelogram Method

All vectors, including the resultant, are drawn from a common origin

The remaining sides of the parallelogram are sketched to determine the diagonal, R

general physics I, lec 1 By: T.A.Eleyan

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Vector Subtraction

Special case of vector addition

If A – B, then use A+(-B)

Continue with standard vector addition procedure

general physics I, lec 1 By: T.A.Eleyan

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Components of a Vector

These are the projections of the vector along the x- and y-axes

general physics I, lec 1 By: T.A.Eleyan

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The x-component of a vector is the projection along the x-axis

The y-component of a vector is the projection along the y-axis

Then,

cosxA A

sinyA A

x yA A A

x

y12y

2x A

AtanandAAA

general physics I, lec 1 By: T.A.Eleyan

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Adding Vectors Algebraically

(1)Choose a coordinate system and sketch the vectors

(2)Find the x- and y-components of all the vector

(3)Add all the x-components

This gives Rx:

xx vR

yy vR

(4)Add all the y-components

This gives Ry

general physics I, lec 1 By: T.A.Eleyan

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(5)find the magnitude of the Resultant

Use the inverse tangent function to find the direction of R:

2y

2x RRR

x

y1

R

Rtan

general physics I, lec 1 By: T.A.Eleyan

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Problem :

Problem: