3 1 Coordinate Systems 1 Cartesian coordinates rectangular

we can obtain the Cartesian coordinates by using the equations: positive θ is an

3. 2 Vector and Scalar Quantities A scalar quantity is completely specified by a

A vector quantity ( or A ) is completely specified by a number and

• Adding Vectors Adding vectors = finding the resultant (R) There are three

Example: If you walked 3. 0 m toward the east and then 4. 0

Geometric construction is Used to add more than two vectors The resultant vector R

Keep in mind that: When two or more vectors are added together, all of

Quick Quiz The magnitudes of two vectors A and B are A = 12

Quick Quiz If vector B is added to vector A, under what condition does

Quick Quiz If vector B is added to vector A, which two of the

Multiplying a Vector by a Scalar If vector A is multiplied by a positive

Example : A car travels 20. 0 km due north and then 35. 0

Quick Quiz Choose the correct response to make the sentence true: A component of

Example Consider a point lying in the xy plane and having Cartesian coordinates (x,

Quick Quiz If at least one component of a vector is a positive number,

Example : The Resultant Displacement A particle undergoes three consecutive displacements: d 1 =

QUESTION (1) Two vectors have unequal magnitudes. Can their sum be zero? Explain. No.

QUESTION (2) Can the magnitude of a particle’s displacement be greater than the distance

QUESTION (5) A vector A lies in the xy plane. For what orientations of

QUESTION (8) If the component of vector A along the direction of vector B

QUESTION (9) Can the magnitude of a vector have a negative value? Explain. No,

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3. 1 Coordinate Systems 1 - Cartesian coordinates (rectangular coordinates). (x, y) 2 - polar coordinate system. (r is the distance an θ is the angle) ﻏﺎﺩﺓ ﻋﻤﻴﺮﺓ. ﺩ ﺟﺎﻣﻌﺔ ﺍﻟﺪﻣﺎﻡ - ﻛﻠﻴﺔ ﺍﻟﺘﺮﺑﻴﺔ ﺑﺎﻟﺠﺒﻴﻞ - 1 ﻓﻴﺰﻳﺎﺀ ﻋﺎﻣﺔ - ﻗﺴﻢ ﺍﻟﻔﻴﺰﻳﺎﺀ

we can obtain the Cartesian coordinates by using the equations: positive θ is an angle measured counterclockwise from the positive ﻋﻤﻴﺮﺓ ﻏﺎﺩﺓ. ﺟﺎﻣﻌﺔ ﺍﻟﺪﻣﺎﻡ ﺩ - ﻛﻠﻴﺔ ﺍﻟﺘﺮﺑﻴﺔ ﺑﺎﻟﺠﺒﻴﻞ - 1 ﻓﻴﺰﻳﺎﺀ ﻋﺎﻣﺔ - ﻗﺴﻢ ﺍﻟﻔﻴﺰﻳﺎﺀ x axis

3. 2 Vector and Scalar Quantities A scalar quantity is completely specified by a single value with an appropriate unit and has no direction. Examples: (volume, mass, speed, distance, time intervals and Temperature). ﻏﺎﺩﺓ ﻋﻤﻴﺮﺓ. ﺩ ﺟﺎﻣﻌﺔ ﺍﻟﺪﻣﺎﻡ - ﻛﻠﻴﺔ ﺍﻟﺘﺮﺑﻴﺔ ﺑﺎﻟﺠﺒﻴﻞ - 1 ﻓﻴﺰﻳﺎﺀ ﻋﺎﻣﺔ - ﻗﺴﻢ ﺍﻟﻔﻴﺰﻳﺎﺀ

A vector quantity ( or A ) is completely specified by a number and appropriate units plus a direction. Examples: (Displacement , velocity, acceleration and area) ﻏﺎﺩﺓ ﻋﻤﻴﺮﺓ. ﺩ ﺟﺎﻣﻌﺔ ﺍﻟﺪﻣﺎﻡ - ﻛﻠﻴﺔ ﺍﻟﺘﺮﺑﻴﺔ ﺑﺎﻟﺠﺒﻴﻞ - 1 ﻓﻴﺰﻳﺎﺀ ﻋﺎﻣﺔ - ﻗﺴﻢ ﺍﻟﻔﻴﺰﻳﺎﺀ

• Adding Vectors Adding vectors = finding the resultant (R) There are three Methods to Adding vectors: 1 - Graphical methods 2 - Algebraically Method. 3 - Vector Analysis ﻏﺎﺩﺓ ﻋﻤﻴﺮﺓ. ﺩ ﺟﺎﻣﻌﺔ ﺍﻟﺪﻣﺎﻡ - ﻛﻠﻴﺔ ﺍﻟﺘﺮﺑﻴﺔ ﺑﺎﻟﺠﺒﻴﻞ - 1 ﻓﻴﺰﻳﺎﺀ ﻋﺎﻣﺔ - ﻗﺴﻢ ﺍﻟﻔﻴﺰﻳﺎﺀ

Example: If you walked 3. 0 m toward the east and then 4. 0 m toward the north, the resultant displacement is 5. 0 m, at an angle of 53° north of east. ﻏﺎﺩﺓ ﻋﻤﻴﺮﺓ. ﺩ ﺟﺎﻣﻌﺔ ﺍﻟﺪﻣﺎﻡ - ﻛﻠﻴﺔ ﺍﻟﺘﺮﺑﻴﺔ ﺑﺎﻟﺠﺒﻴﻞ - 1 ﻓﻴﺰﻳﺎﺀ ﻋﺎﻣﺔ - ﻗﺴﻢ ﺍﻟﻔﻴﺰﻳﺎﺀ

Geometric construction is Used to add more than two vectors The resultant vector R = A + B + C + D is the vector that completes the polygon ﻏﺎﺩﺓ ﻋﻤﻴﺮﺓ. ﺩ ﺟﺎﻣﻌﺔ ﺍﻟﺪﻣﺎﻡ - ﻛﻠﻴﺔ ﺍﻟﺘﺮﺑﻴﺔ ﺑﺎﻟﺠﺒﻴﻞ - 1 ﻓﻴﺰﻳﺎﺀ ﻋﺎﻣﺔ - ﻗﺴﻢ ﺍﻟﻔﻴﺰﻳﺎﺀ

Keep in mind that: When two or more vectors are added together, all of them must have the same units and all of them must be the same type of quantity. ﻏﺎﺩﺓ ﻋﻤﻴﺮﺓ. ﺩ ﺟﺎﻣﻌﺔ ﺍﻟﺪﻣﺎﻡ - ﻛﻠﻴﺔ ﺍﻟﺘﺮﺑﻴﺔ ﺑﺎﻟﺠﺒﻴﻞ - 1 ﻓﻴﺰﻳﺎﺀ ﻋﺎﻣﺔ - ﻗﺴﻢ ﺍﻟﻔﻴﺰﻳﺎﺀ

Quick Quiz The magnitudes of two vectors A and B are A = 12 units and B = 8 units. Which of the following pairs of numbers represents the largest and smallest possible values for the magnitude of the resultant vector R = A + B? (a) 14. 4 units, 4 units (b) 12 units, 8 units (c) 20 units, 4 units (d) none of these answers. ﻏﺎﺩﺓ ﻋﻤﻴﺮﺓ. ﺩ ﺟﺎﻣﻌﺔ ﺍﻟﺪﻣﺎﻡ - ﻛﻠﻴﺔ ﺍﻟﺘﺮﺑﻴﺔ ﺑﺎﻟﺠﺒﻴﻞ - 1 ﻓﻴﺰﻳﺎﺀ ﻋﺎﻣﺔ - ﻗﺴﻢ ﺍﻟﻔﻴﺰﻳﺎﺀ

Quick Quiz If vector B is added to vector A, under what condition does the resultant vector A + B have magnitude A + B? (a) A and B are parallel and in the same direction (b) A and B are parallel and in opposite directions (c) A and B are perpendicular. ﻏﺎﺩﺓ ﻋﻤﻴﺮﺓ. ﺩ ﺟﺎﻣﻌﺔ ﺍﻟﺪﻣﺎﻡ - ﻛﻠﻴﺔ ﺍﻟﺘﺮﺑﻴﺔ ﺑﺎﻟﺠﺒﻴﻞ - 1 ﻓﻴﺰﻳﺎﺀ ﻋﺎﻣﺔ - ﻗﺴﻢ ﺍﻟﻔﻴﺰﻳﺎﺀ

Quick Quiz If vector B is added to vector A, which two of the following choices must be true in order for the resultant vector to be equal to zero? (a) A and B are parallel and in the same direction. (b) A and B are parallel and in opposite directions. (c) A and B have the same magnitude. (d) A and B are perpendicular. ﻏﺎﺩﺓ ﻋﻤﻴﺮﺓ. ﺩ ﺟﺎﻣﻌﺔ ﺍﻟﺪﻣﺎﻡ - ﻛﻠﻴﺔ ﺍﻟﺘﺮﺑﻴﺔ ﺑﺎﻟﺠﺒﻴﻞ - 1 ﻓﻴﺰﻳﺎﺀ ﻋﺎﻣﺔ - ﻗﺴﻢ ﺍﻟﻔﻴﺰﻳﺎﺀ

Multiplying a Vector by a Scalar If vector A is multiplied by a positive scalar quantity m, then the product m. A is a vector that has the same direction as A and magnitude m. A. - If vector A is multiplied by a negative - scalar quantity -m, then the product m. A is directed opposite A. ﻏﺎﺩﺓ ﻋﻤﻴﺮﺓ. ﺩ ﺟﺎﻣﻌﺔ ﺍﻟﺪﻣﺎﻡ - ﻛﻠﻴﺔ ﺍﻟﺘﺮﺑﻴﺔ ﺑﺎﻟﺠﺒﻴﻞ - 1 ﻓﻴﺰﻳﺎﺀ ﻋﺎﻣﺔ - ﻗﺴﻢ ﺍﻟﻔﻴﺰﻳﺎﺀ

Example : A car travels 20. 0 km due north and then 35. 0 km in a direction 60. 0° west of north, as shown in Figure. Find the magnitude and direction of the car’s resultant displacement. Solution 60 B ﻏﺎﺩﺓ ﻋﻤﻴﺮﺓ. ﺩ A ﺟﺎﻣﻌﺔ ﺍﻟﺪﻣﺎﻡ - ﻛﻠﻴﺔ ﺍﻟﺘﺮﺑﻴﺔ ﺑﺎﻟﺠﺒﻴﻞ - 1 ﻓﻴﺰﻳﺎﺀ ﻋﺎﻣﺔ - ﻗﺴﻢ ﺍﻟﻔﻴﺰﻳﺎﺀ

Quick Quiz Choose the correct response to make the sentence true: A component of a vector is (a) always, (b) never, or (c) sometimes larger than the magnitude of the vector. ﻏﺎﺩﺓ ﻋﻤﻴﺮﺓ. ﺩ ﺟﺎﻣﻌﺔ ﺍﻟﺪﻣﺎﻡ - ﻛﻠﻴﺔ ﺍﻟﺘﺮﺑﻴﺔ ﺑﺎﻟﺠﺒﻴﻞ - 1 ﻓﻴﺰﻳﺎﺀ ﻋﺎﻣﺔ - ﻗﺴﻢ ﺍﻟﻔﻴﺰﻳﺎﺀ

Example Consider a point lying in the xy plane and having Cartesian coordinates (x, y), as in Figure. The point can be specified by the position vector r, which in unit–vector form is given by: ﻏﺎﺩﺓ ﻋﻤﻴﺮﺓ. ﺩ ﺟﺎﻣﻌﺔ ﺍﻟﺪﻣﺎﻡ - ﻛﻠﻴﺔ ﺍﻟﺘﺮﺑﻴﺔ ﺑﺎﻟﺠﺒﻴﻞ - 1 ﻓﻴﺰﻳﺎﺀ ﻋﺎﻣﺔ - ﻗﺴﻢ ﺍﻟﻔﻴﺰﻳﺎﺀ

Quick Quiz If at least one component of a vector is a positive number, the vector cannot (a) have any component that is negative (b) be zero (c) have three dimensions. ﻏﺎﺩﺓ ﻋﻤﻴﺮﺓ. ﺩ ﺟﺎﻣﻌﺔ ﺍﻟﺪﻣﺎﻡ - ﻛﻠﻴﺔ ﺍﻟﺘﺮﺑﻴﺔ ﺑﺎﻟﺠﺒﻴﻞ - 1 ﻓﻴﺰﻳﺎﺀ ﻋﺎﻣﺔ - ﻗﺴﻢ ﺍﻟﻔﻴﺰﻳﺎﺀ

Example : The Resultant Displacement A particle undergoes three consecutive displacements: d 1 = (15î + 30ˆj + 12ˆ k) cm, d 2 = (23î - 14ˆj - 5. 0ˆ k) cm and d 3 =(-13î + 15ˆ j) cm. Find the components of the resultant displacement and its magnitude. ﻏﺎﺩﺓ ﻋﻤﻴﺮﺓ. ﺩ ﺟﺎﻣﻌﺔ ﺍﻟﺪﻣﺎﻡ - ﻛﻠﻴﺔ ﺍﻟﺘﺮﺑﻴﺔ ﺑﺎﻟﺠﺒﻴﻞ - 1 ﻓﻴﺰﻳﺎﺀ ﻋﺎﻣﺔ - ﻗﺴﻢ ﺍﻟﻔﻴﺰﻳﺎﺀ

QUESTION (1) Two vectors have unequal magnitudes. Can their sum be zero? Explain. No. The sum of two vectors can only be zero if they are in opposite directions and have the same magnitude. If you walk 10 meters north and then 6 meters south, you won’t end up where you started. ﻏﺎﺩﺓ ﻋﻤﻴﺮﺓ. ﺩ ﺟﺎﻣﻌﺔ ﺍﻟﺪﻣﺎﻡ - ﻛﻠﻴﺔ ﺍﻟﺘﺮﺑﻴﺔ ﺑﺎﻟﺠﺒﻴﻞ - 1 ﻓﻴﺰﻳﺎﺀ ﻋﺎﻣﺔ - ﻗﺴﻢ ﺍﻟﻔﻴﺰﻳﺎﺀ

QUESTION (2) Can the magnitude of a particle’s displacement be greater than the distance traveled? Explain. No, the magnitude of the displacement is always less than or equal to the distance traveled. ﻏﺎﺩﺓ ﻋﻤﻴﺮﺓ. ﺩ ﺟﺎﻣﻌﺔ ﺍﻟﺪﻣﺎﻡ - ﻛﻠﻴﺔ ﺍﻟﺘﺮﺑﻴﺔ ﺑﺎﻟﺠﺒﻴﻞ - 1 ﻓﻴﺰﻳﺎﺀ ﻋﺎﻣﺔ - ﻗﺴﻢ ﺍﻟﻔﻴﺰﻳﺎﺀ

QUESTION (5) A vector A lies in the xy plane. For what orientations of A will both of its components be negative? For what orientations will its components have opposite signs? If the direction-angle of A is between 180 degrees and 270 degrees, its components are both negative. If a vector is in the second quadrant or the fourth quadrant, its components have opposite signs. ﻏﺎﺩﺓ ﻋﻤﻴﺮﺓ. ﺩ ﺟﺎﻣﻌﺔ ﺍﻟﺪﻣﺎﻡ - ﻛﻠﻴﺔ ﺍﻟﺘﺮﺑﻴﺔ ﺑﺎﻟﺠﺒﻴﻞ - 1 ﻓﻴﺰﻳﺎﺀ ﻋﺎﻣﺔ - ﻗﺴﻢ ﺍﻟﻔﻴﺰﻳﺎﺀ

QUESTION (8) If the component of vector A along the direction of vector B is zero, what can you conclude about the two vectors? Vectors A and B are perpendicular to each other. ﻏﺎﺩﺓ ﻋﻤﻴﺮﺓ. ﺩ ﺟﺎﻣﻌﺔ ﺍﻟﺪﻣﺎﻡ - ﻛﻠﻴﺔ ﺍﻟﺘﺮﺑﻴﺔ ﺑﺎﻟﺠﺒﻴﻞ - 1 ﻓﻴﺰﻳﺎﺀ ﻋﺎﻣﺔ - ﻗﺴﻢ ﺍﻟﻔﻴﺰﻳﺎﺀ

QUESTION (9) Can the magnitude of a vector have a negative value? Explain. No, the magnitude of a vector is always positive. A minus sign in a vector only indicates direction, not magnitude. ﻏﺎﺩﺓ ﻋﻤﻴﺮﺓ. ﺩ ﺟﺎﻣﻌﺔ ﺍﻟﺪﻣﺎﻡ - ﻛﻠﻴﺔ ﺍﻟﺘﺮﺑﻴﺔ ﺑﺎﻟﺠﺒﻴﻞ - 1 ﻓﻴﺰﻳﺎﺀ ﻋﺎﻣﺔ - ﻗﺴﻢ ﺍﻟﻔﻴﺰﻳﺎﺀ