Scalars and Vectors

• The motion of objects can be described by words. – going fast, stopped, slowing down, speeding

up, and turning provide a sufficient vocabulary for describing the motion of objects.

– In physics, we use these words and many more. We will be expanding upon this vocabulary list with words such as distance, displacement, speed, velocity, and acceleration.

Vector

• A vector has – magnitude as well as direction, and – vectors follow certain (vector) rules of

combination.– A vector quantity is a quantity that has both

a magnitude and a direction and thus can be represented with a vector. Some physical quantities that are vector quantities are displacement, velocity, and acceleration.

Scalar

• A Scalar has – Involved Magnitude only. – Not involved a direction.– Temperature, pressure, energy, mass, and

time, for example, do not "point" in the spatial sense.

– We call such quantities scalars, and we deal with them by the rules of ordinary algebra.

In short

– Scalars are quantities that are fully described by a magnitude (or numerical value) alone.

– Vectors are quantities that are fully described by both a magnitude and a direction.

Vector

• A vector is a quantity that has both magnitude and direction. The magnitude is a scalar quantity, a scalar being defined as a quantity which may be completely specified by a number and perhaps a unit. Common textbook representations of vectors include boldfaced letters and boldface with an arrow above them. For example a displacement vector of 30 meters east could be represented in a variety of ways:

The magnitude of the vector might be represented by absolute value signs around the vector symbol, or just the letter without the boldface.

A vector might also be expressed in terms of unit vectors.

Check your understanding??

Quantity Category

5 m

30 m/sec, East

5 mi., North

20 degrees Celsius

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Example

• Distance and displacement are two quantities that may seem to mean the same thing yet have distinctly different definitions and meanings.

• Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.

• Displacement is a vector quantity that refers to "how far out of place an object is"; it is the object's overall change in position.

• distance = 12 m; displacement = 0

Adding vector geometrically

• AC is the vector sum of the vectors AB and BC.

Adding vector geometrically

Components of Vector

Unit Vector

Self study

• Sample Problem

• Sample Problem

Vectors and Laws of Physics

Multiplying Vectors

• Scalar Product

Appendix

Appendix

Try Urself

• A hiker takes a trip involving three segment path A is 20m long at a direction of 30 degree N of E, path B is 30m due East, path C is 5m long at a direction of 45 degree E of S. Find the resultant displacement?

Good Luck!!!