Vectors. A VECTOR? □Describes the motion of an object □A Vector comprises □Direction...

20
Vectors

TAGS:

Transcript of Vectors. A VECTOR? □Describes the motion of an object □A Vector comprises □Direction...

Page 1: Vectors. A VECTOR? □Describes the motion of an object □A Vector comprises □Direction □Magnitude □We will consider □Column VectorsColumn Vectors □General.

Vectors

Page 2: Vectors. A VECTOR? □Describes the motion of an object □A Vector comprises □Direction □Magnitude □We will consider □Column VectorsColumn Vectors □General.

A VECTOR?

□Describes the motion of an object□A Vector comprises

□Direction□Magnitude

□We will consider□Column Vectors□General Vectors□Vector Geometry

Size

Page 3: Vectors. A VECTOR? □Describes the motion of an object □A Vector comprises □Direction □Magnitude □We will consider □Column VectorsColumn Vectors □General.

Column Vectors

a

Vector a

COLUMN Vector

4 RIGHT

2 up

NOTE!

Label is in BOLD.

When handwritten, draw a wavy line under the label

i.e.

Page 4: Vectors. A VECTOR? □Describes the motion of an object □A Vector comprises □Direction □Magnitude □We will consider □Column VectorsColumn Vectors □General.

Column Vectors

b

Vector b

COLUMN Vector?

3 LEFT

2 up

Page 5: Vectors. A VECTOR? □Describes the motion of an object □A Vector comprises □Direction □Magnitude □We will consider □Column VectorsColumn Vectors □General.

Column Vectors

n

Vector u

COLUMN Vector?

4 LEFT

2 down

Page 6: Vectors. A VECTOR? □Describes the motion of an object □A Vector comprises □Direction □Magnitude □We will consider □Column VectorsColumn Vectors □General.

Describe these vectors

b

a

c

d

Page 7: Vectors. A VECTOR? □Describes the motion of an object □A Vector comprises □Direction □Magnitude □We will consider □Column VectorsColumn Vectors □General.

Alternative labelling

A

B

C

DF

E

G

H

Page 8: Vectors. A VECTOR? □Describes the motion of an object □A Vector comprises □Direction □Magnitude □We will consider □Column VectorsColumn Vectors □General.

General VectorsA Vector has BOTH a Length & a Direction

k can be in any position

k

k

k

k

All 4 Vectors here are EQUAL in Length andTravel in SAME Direction.All called k

Page 9: Vectors. A VECTOR? □Describes the motion of an object □A Vector comprises □Direction □Magnitude □We will consider □Column VectorsColumn Vectors □General.

General Vectors

kA

B

C

D

-k

2k

F

E

Line CD is Parallel to AB

CD is TWICE length of AB

Line EF is Parallel to AB

EF is equal in length to AB

EF is opposite direction to AB

Page 10: Vectors. A VECTOR? □Describes the motion of an object □A Vector comprises □Direction □Magnitude □We will consider □Column VectorsColumn Vectors □General.

Write these Vectors in terms of k

k

A

B

C

D

E

F G

H

2k1½k ½k

-2k

Page 11: Vectors. A VECTOR? □Describes the motion of an object □A Vector comprises □Direction □Magnitude □We will consider □Column VectorsColumn Vectors □General.

Combining Column Vectors

k

A

B

C

D

Page 12: Vectors. A VECTOR? □Describes the motion of an object □A Vector comprises □Direction □Magnitude □We will consider □Column VectorsColumn Vectors □General.

A

B

C

Simple combinations

Page 13: Vectors. A VECTOR? □Describes the motion of an object □A Vector comprises □Direction □Magnitude □We will consider □Column VectorsColumn Vectors □General.

Vector GeometryConsider this parallelogram

Q

O

P

Ra

b

Opposite sides are Parallel

OQ is known as the resultant of a and b

Page 14: Vectors. A VECTOR? □Describes the motion of an object □A Vector comprises □Direction □Magnitude □We will consider □Column VectorsColumn Vectors □General.

Resultant of Two Vectors

□Is the same, no matter which route is followed

□Use this to find vectors in geometrical figures

Page 15: Vectors. A VECTOR? □Describes the motion of an object □A Vector comprises □Direction □Magnitude □We will consider □Column VectorsColumn Vectors □General.

Example

Q

O

P

Ra

b

.SS is the Midpoint of PQ.

Work out the vector

= a + ½b

Page 16: Vectors. A VECTOR? □Describes the motion of an object □A Vector comprises □Direction □Magnitude □We will consider □Column VectorsColumn Vectors □General.

Alternatively

Q

O

P

Ra

b

.SS is the Midpoint of PQ.

Work out the vector

= a + ½b

= b + a - ½b

= ½b + a

Page 17: Vectors. A VECTOR? □Describes the motion of an object □A Vector comprises □Direction □Magnitude □We will consider □Column VectorsColumn Vectors □General.

Example

AB

C

p

q

M M is the Midpoint of BC

Find BC

AC= p, AB = q

BC BA AC= += -q + p

= p - q

Page 18: Vectors. A VECTOR? □Describes the motion of an object □A Vector comprises □Direction □Magnitude □We will consider □Column VectorsColumn Vectors □General.

Example

AB

C

p

q

M M is the Midpoint of BC

Find BM

AC= p, AB = q

BM ½BC=

= ½(p – q)

Page 19: Vectors. A VECTOR? □Describes the motion of an object □A Vector comprises □Direction □Magnitude □We will consider □Column VectorsColumn Vectors □General.

Example

AB

C

p

q

M M is the Midpoint of BC

Find AM

AC= p, AB = q

= q + ½(p – q)

AM + ½BC= AB

= q +½p - ½q

= ½q +½p = ½(q + p) = ½(p + q)

Page 20: Vectors. A VECTOR? □Describes the motion of an object □A Vector comprises □Direction □Magnitude □We will consider □Column VectorsColumn Vectors □General.

Alternatively

AB

C

p

q

M M is the Midpoint of BC

Find AM

AC= p, AB = q

= p + ½(q – p)

AM + ½CB= AC

= p +½q - ½p

= ½p +½q = ½(p + q)


Ch 3 Vectors. Vectors What is the difference between a scalar and a vector? A vector is a physical quantity that has both magnitude and direction What.

Ch 3 Vectors. Vectors What is the difference between a scalar and a vector? A vector is a physical quantity that has both magnitude and direction What.

Vectors Vector: quantity that has magnitude and direction Scalar: quantity that has magnitude only –Example: 20 mi north (vector) vs. 20 mi (scalar) Arrows.

Vectors Vector: quantity that has magnitude and direction Scalar: quantity that has magnitude only –Example: 20 mi north (vector) vs. 20 mi (scalar) Arrows.

VECTORSVECTORS Vectors and Scalars A vector has magnitude as well as direction. Some vector quantities: displacement, velocity, force, momentum.

VECTORSVECTORS Vectors and Scalars A vector has magnitude as well as direction. Some vector quantities: displacement, velocity, force, momentum.

UNIT 1 DYNAMICS. SCALARS & VECTORS Scalar - has magnitude only ! eg. Speed, distance Vector - has magnitude and direction. eg. Velocity, Acceleration.

UNIT 1 DYNAMICS. SCALARS & VECTORS Scalar - has magnitude only ! eg. Speed, distance Vector - has magnitude and direction. eg. Velocity, Acceleration.

Regents Physics Review #1 Vectors - · PDF fileRegents Physics Review #1 Vectors . Scalar Vector Magnitude(size) only Magnitude (size) AND ... The projectile reaches its highest point

Regents Physics Review #1 Vectors - · PDF fileRegents Physics Review #1 Vectors . Scalar Vector Magnitude(size) only Magnitude (size) AND ... The projectile reaches its highest point

Vectors and Linear Motion. Vector Quantities: Have a magnitude And direction ex: meters, velocity, acceleration Scalar Quantities: Have only a magnitude.

Vectors and Linear Motion. Vector Quantities: Have a magnitude And direction ex: meters, velocity, acceleration Scalar Quantities: Have only a magnitude.

FAD -01 Vectors. Vector or Scalar A vector quantity has both direction and magnitude (size). In contrast a scalar quantity has magnitude only.

FAD -01 Vectors. Vector or Scalar A vector quantity has both direction and magnitude (size). In contrast a scalar quantity has magnitude only.

Vectors and Vector Multiplication. Vector quantities are those that have magnitude and direction, such as: Displacement, x or Velocity, Acceleration,

Vectors and Vector Multiplication. Vector quantities are those that have magnitude and direction, such as: Displacement, x or Velocity, Acceleration,

Vectors in 2 and 3 dimensions Definition: A scalar has magnitude A vector has magnitude and direction.

Vectors in 2 and 3 dimensions Definition: A scalar has magnitude A vector has magnitude and direction.

Vectors Vector quantity has direction as well as magnitude.

Vectors Vector quantity has direction as well as magnitude.

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.

Ch. 3, Kinematics in 2 Dimensions; Vectors. Vectors General discussion. Vector A quantity with magnitude & direction. Scalar A quantity with magnitude.

Ch. 3, Kinematics in 2 Dimensions; Vectors. Vectors General discussion. Vector A quantity with magnitude & direction. Scalar A quantity with magnitude.

Vectors All vector quantities have magnitude (size) and direction. Vectors in physics that we will use: Force, displacement, velocity, and acceleration.

Vectors All vector quantities have magnitude (size) and direction. Vectors in physics that we will use: Force, displacement, velocity, and acceleration.

KD1 Vectors. Scalar vs. Vector Scalar-Quantity having magnitude only (no direction) Ex: Temp., mass, time, speed Vector-Quantity having magnitude AND.

KD1 Vectors. Scalar vs. Vector Scalar-Quantity having magnitude only (no direction) Ex: Temp., mass, time, speed Vector-Quantity having magnitude AND.

Mechanics: Scalars and Vectors Notes/ME101-Lecture02-KD.pdf · Mechanics: Scalars and Vectors A Vector V can be written as: V = Vn V = magnitude of V n = unit vector whose magnitude

Mechanics: Scalars and Vectors Notes/ME101-Lecture02-KD.pdf · Mechanics: Scalars and Vectors A Vector V can be written as: V = Vn V = magnitude of V n = unit vector whose magnitude

CHAPTER 3 Two-Dimensional Motion and Vectors. Representations: x y (x, y) (r, ) VECTOR quantities: Vectors have magnitude and direction. Other vectors:

CHAPTER 3 Two-Dimensional Motion and Vectors. Representations: x y (x, y) (r, ) VECTOR quantities: Vectors have magnitude and direction. Other vectors:

Vectors: Resolution and Addition. Vectors: The Basics Vector: has both magnitude and direction – Examples: displacement, velocity, acceleration Scalar:

Vectors: Resolution and Addition. Vectors: The Basics Vector: has both magnitude and direction – Examples: displacement, velocity, acceleration Scalar:

Vectors 9.7 Chapter 9 Right Triangles and Trigonometry Section 9.7 Vectors Find the magnitude and the direction of a vector. Add vectors.

Vectors 9.7 Chapter 9 Right Triangles and Trigonometry Section 9.7 Vectors Find the magnitude and the direction of a vector. Add vectors.

Unit Vectors & Direction Angles - goblues.orggoblues.org/.../files/2010/08/Unit-Vectors-Direction-Angles.pdf · What is a unit vector?! A vector with a magnitude of 1.! What are the

Unit Vectors & Direction Angles - goblues.orggoblues.org/.../files/2010/08/Unit-Vectors-Direction-Angles.pdf · What is a unit vector?! A vector with a magnitude of 1.! What are the

Vectors A vector is basically an arrow that represents the magnitude and direction of a measurement. The length of the vector represents its magnitude.

Vectors A vector is basically an arrow that represents the magnitude and direction of a measurement. The length of the vector represents its magnitude.