Presentation is loading. Please wait.

Presentation is loading. Please wait.

Vectors A vector quantity has both magnitude (size) and direction A scalar quantity only has size (i.e. temperature, time, energy, etc.) Parts of a vector:

Published byOphelia Allison Modified over 8 years ago

Similar presentations

Presentation on theme: "Vectors A vector quantity has both magnitude (size) and direction A scalar quantity only has size (i.e. temperature, time, energy, etc.) Parts of a vector:"— Presentation transcript:

1 Vectors A vector quantity has both magnitude (size) and direction A scalar quantity only has size (i.e. temperature, time, energy, etc.) Parts of a vector: headtail length – represents the magnitude We can perform math operations with vectors!

2 Vector Addition A motor boat is moving 15 km/hr relative to the water. The river current is 10 km/hr downstream. How fast does the boat go (relative to the shore) upstream and downstream? Boat Upstream Vector

3 Vector Addition A motor boat is moving 15 km/hr relative to the water. The river current is 10 km/hr downstream. How fast does the boat go (relative to the shore) upstream and downstream? Boat Upstream Vector Boat Downstream Vector

4 Vector Addition A motor boat is moving 15 km/hr relative to the water. The river current is 10 km/hr downstream. How fast does the boat go (relative to the shore) upstream and downstream? Current Vector = 10 km/hr downstream Boat Upstream Vector Boat Downstream Vector

5 Boat Velocity Upstream Upstream: Place vectors head to tail, net result, 5 km/hr upstream

6 Boat Velocity Upstream Upstream: Place vectors head to tail,

7 Boat Velocity Upstream: Place vectors head to tail, net result, 5 km/hr upstream Start Finish Difference

8 Boat Velocity Downstream: Place vectors head to tail,

9 Boat Velocity Downstream: Place vectors head to tail, net result,

10 Boat Velocity Downstream: Place vectors head to tail, net result, 25 km/hr downstream Commutative law

11 Forces On An Airplane When will it fly? Gravity Propulsion Net Force?

12 Forces On An Airplane When will it fly? Gravity Propulsion Net Force Plane Dives to the Ground

13 Forces On An Airplane When will it fly? Gravity Propulsion Lift Net Force?

14 Friction When will it fly? Gravity Propulsion Lift Net Force = 0 up or down Plane rolls along the runway like a car because of propulsion.

15 Forces On An Airplane When will it fly? Gravity Propulsion Lift Net Force Plane Flies as long as Lift > Gravity

16 Friction When will it fly? Gravity Propulsion Lift Air Resistance Net Force = 0 Equilibrium

17 Flight When will it fly? Gravity Propulsion Lift Air Resistance Net Force Plane Flies as long as Lift > Gravity AND Propulsion > Air Resistance

18 Vector Components A component of a vector is the projection of the vector on an axis x y Magnitude, size is: We can write the vector A as the sum of an x-component and y-component: A x, A y = the x and y components of the vector A x hat and and y hat are the unit vectors

19 x y  If we only know the mag. of A, and the angle,  it makes with the x-axis, how do we find the x, and y components?

20 x y  If we only know the x and y components, how can we find the magnitude of A? This comes from Pythagorean’s theorem GO TO HITT

21 Adding (and subtracting) vectors by components Let’s say I have two vectors: I want to calculate the vector sum of these vectors: Let’s say the vectors have the following values:

22 A B A B Our result is consistent with the graphical method! What’s the magnitude of our new vector?

23 A B + How would you find the angle, , the vector makes with the y-axis?  opp = 2  adj = 12 GO TO HITT

24 Multiplying vectors by scalars: So if the vector A was: the scalar, a = 5 then the new vector: and it was multiplied by Scalar Product: (aka dot product): mag. of a mag. of b angle between the vectors

25 Scalar Product: (aka dot product): vectors scalars The dot product is the product of two quantities: (1)mag. of one vector (2)scalar component of the second vector along the direction of the first Go To HITT

26 Vector Product (aka cross product) The vector product produces a new vector who’s magnitude is given by: The direction of the new vector is given by the, “right hand rule” Mathematically, we can find the direction using matrix operations. The cross product is determined from three determinants

27 The determinants are used to find the components of the vector 1 st : Strike out the first column and first row! 3 rd : Strike out the 2 nd column and first row 4 th : Cross multiply the four components,subtract, and multiply by -1: 2 nd : Cross multiply the four components – and subtract: x - component y - component

28 5 th : Cross out the last column and first row 6 th : Cross multiply and subtract four elements z-component So then the new vector will be: We’ll look more at the scalar product when we talk about angular momentum. Example:

29 Notice the resultant vector is in the z – direction!

Download ppt "Vectors A vector quantity has both magnitude (size) and direction A scalar quantity only has size (i.e. temperature, time, energy, etc.) Parts of a vector:"

Similar presentations

General Physics (PHYS101)

General Physics (PHYS101)
Rolling, Torque, and Angular Momentum Rolling: Translation and Rotation Friction and Rolling Yo-yo Torque: A Cross Product Angular Momentum Newton’s Second.

Rolling, Torque, and Angular Momentum Rolling: Translation and Rotation Friction and Rolling Yo-yo Torque: A Cross Product Angular Momentum Newton’s Second.
3.1 Introduction to Vectors

3.1 Introduction to Vectors
Projectile Motion Chapter 5.

Projectile Motion Chapter 5.
VECTORS Computer Graphics. A REVIEW OF VECTORS:  Scalar Quantity  Vector Quantity  2D vectors  Graphical Representation of Vectors  Magnitude of.

VECTORS Computer Graphics. A REVIEW OF VECTORS:  Scalar Quantity  Vector Quantity  2D vectors  Graphical Representation of Vectors  Magnitude of.
Vectors: 5 Minute Review Vectors can be added or subtracted. ◦ To add vectors graphically, draw one after the other, tip to tail. ◦ To add vectors algebraically,

Vectors: 5 Minute Review Vectors can be added or subtracted. ◦ To add vectors graphically, draw one after the other, tip to tail. ◦ To add vectors algebraically,
Vectors and Scalars Vector and scalar quantities Adding vectors geometrically Components Unit Vectors Dot Products Cross Products pps by C Gliniewicz.

Vectors and Scalars Vector and scalar quantities Adding vectors geometrically Components Unit Vectors Dot Products Cross Products pps by C Gliniewicz.
Chapter 3: VECTORS 3-2 Vectors and Scalars 3-2 Vectors and Scalars

Chapter 3: VECTORS 3-2 Vectors and Scalars 3-2 Vectors and Scalars
Vectors: 5 Minute Review Vectors can be added or subtracted. ◦ To add vectors graphically, draw one after the other, tip to tail. ◦ To add vectors algebraically,

Vectors: 5 Minute Review Vectors can be added or subtracted. ◦ To add vectors graphically, draw one after the other, tip to tail. ◦ To add vectors algebraically,
Scalar and Vector Fields

Scalar and Vector Fields
Vectors.

Vectors.
Chapter 3. Vector 1. Adding Vectors Geometrically

Chapter 3. Vector 1. Adding Vectors Geometrically
Definitions Examples of a Vector and a Scalar More Definitions

Definitions Examples of a Vector and a Scalar More Definitions
AP Physics C Vector review and 2d motion The good news You will follow all of the same rules you used in 1d motion. It allows our problems to more realistic.

AP Physics C Vector review and 2d motion The good news You will follow all of the same rules you used in 1d motion. It allows our problems to more realistic.
Vectors Vector: a quantity that has both magnitude (size) and direction Examples: displacement, velocity, acceleration Scalar: a quantity that has no.

Vectors Vector: a quantity that has both magnitude (size) and direction Examples: displacement, velocity, acceleration Scalar: a quantity that has no.
Phys211C1V p1 Vectors Scalars: a physical quantity described by a single number Vector: a physical quantity which has a magnitude (size) and direction.

Phys211C1V p1 Vectors Scalars: a physical quantity described by a single number Vector: a physical quantity which has a magnitude (size) and direction.
Vectors This is one of the most important chapters in the course. PowerPoint presentations are compiled from Walker 3 rd Edition Instructor CD-ROM and.

Vectors This is one of the most important chapters in the course. PowerPoint presentations are compiled from Walker 3 rd Edition Instructor CD-ROM and.
Vectors Vector: a quantity that has both magnitude (size) and direction Examples: displacement, velocity, acceleration Scalar: a quantity that has no.

Vectors Vector: a quantity that has both magnitude (size) and direction Examples: displacement, velocity, acceleration Scalar: a quantity that has no.
Vectors. Definitions Scalar – magnitude only Vector – magnitude and direction I am traveling at 65 mph – speed is a scalar. It has magnitude but no direction.

Vectors. Definitions Scalar – magnitude only Vector – magnitude and direction I am traveling at 65 mph – speed is a scalar. It has magnitude but no direction.
Vectors. Vectors and Direction Vectors are quantities that have a size and a direction. Vectors are quantities that have a size and a direction. A quantity.

Vectors. Vectors and Direction Vectors are quantities that have a size and a direction. Vectors are quantities that have a size and a direction. A quantity.

Similar presentations

Ads by Google