Vector and Scaler Chapter 2 PDF

MOHAMMED AL-MANA COLLEGE FOR MEDICAL SCIENCES Chapter2:SCALARS&VECTORS Dr. Ohoud Aljawi MOHAMMED AL-MANA COLLEGE FOR MEDICAL SCIENCES LEARNING OUTCOMES • Differentiate between vector and scalar quantities • Apply addition of vectors by Head to Tail method (Graphical Method) • Apply subtraction o...

MOHAMMED AL-MANA COLLEGE FOR MEDICAL SCIENCES Chapter2:SCALARS&VECTORS Dr. Ohoud Aljawi MOHAMMED AL-MANA COLLEGE FOR MEDICAL SCIENCES LEARNING OUTCOMES • Differentiate between vector and scalar quantities • Apply addition of vectors by Head to Tail method (Graphical Method) • Apply subtraction of vectors, and multiplication of a vector by a scalar • Apply multiplication of two vectors MOHAMMED AL-MANA COLLEGE FOR MEDICAL SCIENCES 2.1 SCALARS & VECTORS A. SCALAR QUANTITIES: https://www.youtube.com/watch?v=Pj8Zh0A-uLU&t=6s A scalar quantity that can completely be described by a magnitude (size) and having an appropriate unit. Example for scalars quantities Work Distance Energy Area Electric Flux Density Volume Temperature Time Speed MOHAMMED AL-MANA COLLEGE FOR MEDICAL SCIENCES 2.1 SCALARS & VECTORS A. SCALAR QUANTITIES: When scalars are added the total is simply the arithmetic total. Example: If there are two masses of 2.4 Kg and 5.2 kg, the total mass is 7.6 kg. 2.4 Kg 5.2 Kg Adding two scalar quantities must be in the same unit 2m +5 m = 7m (correct) 4m + 3 kg = no answer 7.6 Kg 2.1 SCALARS & VECTORS MOHAMMED AL-MANA COLLEGE FOR MEDICAL SCIENCES VECTORS QUANTITIES Example of vector quantities TODAY'S QUOTE Velocity Electric and Magnetic Field Intensity Acceleration Force Weight Momentum Impulse Pressure Torque Displacement Electric intensity 2.1 SCALARS & VECTORS MOHAMMED AL-MANA COLLEGE FOR MEDICAL SCIENCES B. VECTORS QUANTITIES: ❖ ❖ Vector quantity has both magnitude (size), a direction and unit. Vector quantities are represented by a straight line with arrow head pointing the direction of vector. It expressed by using bold letters with arrow sign such as TODAY'S QUOTE ❖ 2.1 SCALARS & VECTORS MOHAMMED AL-MANA COLLEGE FOR MEDICAL SCIENCES B. VECTORS QUANTITIES: When vectors are added their direction must be taken into account. Example: Two forces of 3N and 5N acting in the same directions would give a total force of 8N. TODAY'S QUOTE 3N 5N 8N If they act in opposite directions the total force (5- 3) N = 2N 5N 3N 2N If they act at any other angle to each other the triangle of vector is used MOHAMMED AL-MANA COLLEGE FOR MEDICAL SCIENCES 1 2 3 MOHAMMED AL-MANA COLLEGE FOR MEDICAL SCIENCES Example: 1- Addition vector What is the net displacement for the following vectors? R P Q Q MOHAMMED AL-MANA COLLEGE FOR MEDICAL SCIENCES Example: What is the net displacement for the following vectors? R P Q MOHAMMED AL-MANA COLLEGE FOR MEDICAL SCIENCES 2- Subtraction of Vectors: In order to subtract vectors, we define the negative of a vector, which has the same magnitude but points in the opposite direction. Example MOHAMMED AL-MANA COLLEGE FOR MEDICAL SCIENCES Example: What is the net resultant vectors in the following diagram? MOHAMMED AL-MANA COLLEGE FOR MEDICAL SCIENCES Example: What is the net resultant vectors in the following diagram? MOHAMMED AL-MANA COLLEGE FOR MEDICAL SCIENCES 3- Multiplication of a Vector by a Scalar A vector V can be multiplied by a scalar c; the result is a vector cV that has the same direction but a magnitude cV. If c is negative, the resultant vector points in the opposite direction. Example V c = 1.2 MOHAMMED AL-MANA COLLEGE FOR MEDICAL SCIENCES 2.1 SCALARS & VECTORS Exercise 1- If a time is multiplied by a velocity, is the resultant quantity a vector quantity or a scalar quantity? For example the car is moving 5 m/s west during 2 second A. Vector Quantity B. Scalar Quantity MOHAMMED AL-MANA COLLEGE FOR MEDICAL SCIENCES 2.1 SCALARS & VECTORS Exercise 2- If a speed is multiplied by a time, is the resultant quantity a vector quantity or a scalar quantity? A. Vector quantity B. Scalar quantity MOHAMMED AL-MANA COLLEGE FOR MEDICAL SCIENCES 2.1 SCALARS & VECTORS Exercise 3- If an acceleration is multiplied by a time, is the resultant quantity a vector quantity or a scalar quantity? A. Vector quantity B. Scalar quantity 2.3 Component of vectors MOHAMMED AL-MANA COLLEGE FOR MEDICAL SCIENCES 2.3 Component of vectors MOHAMMED AL-MANA COLLEGE FOR MEDICAL SCIENCES To find the Magnitude (size)by using equation 1 and direction of the vector, by using equation 2: (1) (2) 2.3 Component of vectors a) 𝑨𝒙 = 𝟑 , 𝑨𝒚 = 𝟐 b) 𝑨𝒙 = −𝟑 , 𝑨𝒚 = −𝟐 MOHAMMED AL-MANA COLLEGE FOR MEDICAL SCIENCES 2.3 Component of vectors MOHAMMED AL-MANA COLLEGE FOR MEDICAL SCIENCES Find the Magnitude for vector 𝐴 ? a) 3.60 b) 3.60 2.3 Component of vectors a) 𝑨𝒙 = 𝟑 , 𝑨𝒚 = 𝟐 b) 𝑨𝒙 = −𝟑 , 𝑨𝒚 = −𝟐 MOHAMMED AL-MANA COLLEGE FOR MEDICAL SCIENCES 𝜽= 𝜽= 𝒕𝒂𝒏−𝟏 𝒕𝒂𝒏−𝟏 𝟐 = 𝟑𝟑. 𝟕° 𝟑 −𝟐 = 𝟑𝟑. 𝟕° −𝟑 2.4 unit vector MOHAMMED AL-MANA COLLEGE FOR MEDICAL SCIENCES 2.4 unit vector MOHAMMED AL-MANA COLLEGE FOR MEDICAL SCIENCES 𝐴 = 𝐴𝑥 𝑖 + 𝐴𝑦 𝑗, 𝐵 = 𝐵𝑥 𝑖 + 𝐵𝑦 𝑗 Group Work MOHAMMED AL-MANA COLLEGE FOR MEDICAL SCIENCES 2.5 Multiplication of two vectors MOHAMMED AL-MANA COLLEGE FOR MEDICAL SCIENCES There are two types of the multiplication of two vectors: • Scalar product or dot product • Vector product or cross product 2.5 Multiplication of two vectors MOHAMMED AL-MANA COLLEGE FOR MEDICAL SCIENCES 2.5 Multiplication of two vectors Example: MOHAMMED AL-MANA COLLEGE FOR MEDICAL SCIENCES 2.5 Multiplication of two vectors Example: MOHAMMED AL-MANA COLLEGE FOR MEDICAL SCIENCES 2.5 Multiplication of two vectors MOHAMMED AL-MANA COLLEGE FOR MEDICAL SCIENCES 2.5 Multiplication of two vectors Example: MOHAMMED AL-MANA COLLEGE FOR MEDICAL SCIENCES 2.5 Multiplication of two vectors MOHAMMED AL-MANA COLLEGE FOR MEDICAL SCIENCES Example: When we multiply two vector quantities moment arm (distance) and force we get torque which is also a vector quantity. Therefore, we can say that torque is the vector product or cores product of the 2.5 Multiplication of two vectors MOHAMMED AL-MANA COLLEGE FOR MEDICAL SCIENCES A. VECTOR PRODUCT OR CROSS PRODUCT Exercise: Calculate a × b when a = 2, b = 4 and the angle between a and b is θ = 45 a × b = 5.6 MOHAMMED AL-MANA COLLEGE FOR MEDICAL SCIENCES THANK YOU CONTACT INFORMATION E-MAIL: [email protected] Office Hours: 08:00 - 04:00