Two-Dimensional Motion and Vectors

Chapter 02

Honors Physics Longmeadow High School

Chapter 02 – Two-Dimensional Motion and Vectors

2-1 Scalars and Vectors Defined

Chapter 02 – Two-Dimensional Motion and Vectors

• A scalar quantity is a physical quantity that can be completely described by its magnitude

• A vector quantity is a physical quantity with both a magnitude and a directed associated with it

2-2 Examples of Scalar and Vector Quantities

Chapter 02 – Two-Dimensional Motion and Vectors

Scalars Vectors

Temperature (˚F or ˚C) Displacement (m)

Number of Gas Molecules in a Container Velocity (m/s)

Volume (m3) Acceleration (m/s2)

Mass (kg) Force (N)

Distance (m) Momentum (kg·m/s)

Speed (m/s) Torque (N·m)

Work (J) Electric Field (N/C)

Power (W)

Kinetic Energy (J)

Potential Energy (J)

Electric Charge (C)

Electric Current (A)

2-3 Representing Vectors

Chapter 02 – Two-Dimensional Motion and Vectors

• Textbook and Typed Media– Boldface indicates a vector quantity• v = 3.5 m/s at 30˚

– Italics indicate a scalar quantity• v = 3.5 m/s where v = |v|

• Handwritten / Blackboard– Arrow above abbreviation indicates vector

quantity• v = 3.5 m/s at North

2-4 Describing Vectors Graphically

Chapter 02 – Two-Dimensional Motion and Vectors

• Vectors are depicted as arrows with the tip of the arrow indicating the direction of the vector

• A vector has both a tail and a tip• The length of the arrow is proportional to its

magnitude• The direction of a vector is typically given with

respect to the horizontal axis “…walks 5 km 30˚ north of east”

• Be on the look out for alternative descriptions “east of north”

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2-5 Resolving Vectors into Components

Chapter 02 – Two-Dimensional Motion and Vectors

2-6 Combining Scalars and Vectors

Chapter 02 – Two-Dimensional Motion and Vectors

Vector quantities are distinct from scalar quantities – they combine differently.

We’re used to combining scalars:– The sum of two scalars results in a: scalar– The product of two scalars results in a: scalar

Now consider vectors – they can combine with scalars as well as with other vectors– The sum of two vectors results in a: vector

– The product of a scalar and a vector results in a: vectorThink about what “scaling” a vector might look like

– The product of two vectors results in: well, that dependsThere are not one, but two different ways in which to multiply vectors – one resulting

in a scalar (scalar product) and another resulting in a vector (vector product)

2-7 Scalar Multiplication

Chapter 02 – Two-Dimensional Motion and Vectors

Negative of a Vector

2-8 Vector Addition: Parallelogram Method

Chapter 02 – Two-Dimensional Motion and Vectors

• Draw vectors A and B such that they share a common tail.• Taking these two vectors to be two adjacent sides of a

parallelogram, draw the resultant vector as the diagonal

2-9 Vector Addition: Tail-to-Tip/Head-To-Tail Method

Chapter 02 – Two-Dimensional Motion and Vectors

• Start by placing any vector with its tail at the origin• Place the tail of the next vector to the tip of the previous

vector• After doing this for all vectors, the resultant vector is

found by drawing a straight line from the tail of the first vector to the tip of the last vector.