What is Physics?

n From Greek word ‘physis’ (nature) and physike(knowledge of nature).

n Physics is a natural science based on experiments, measurements and mathematical analysis with the purpose of finding quantitative physical laws for everything from microcosmos (nano world) to macrocosmos (universe).

n Physics is described as the study of matter and energy. It is concerned with how matter and energy relate to each other, and how they affect each other over time and through space.

Experimental and Theoretical physicists.n Physicists may be roughly divided into two groups:

experimental physicists and theoretical physicists.

q Experimental physicists design and run careful investigations on a broad range of phenomena in nature,

q Theoretical physicists: propose and develop models and theories to explain mathematically the results of experimental observations.

Classical physics and Modern physics

n Classical physics q has its origins approximately 400 years ago in the studies of

Galileo and Newton on mechanics, and similarly in the work of Ampere, Faraday, and Maxwell 150 years ago in the fields of electricity and magnetism. This physics handles objects which are neither too large nor too small, which move at relatively slow speeds compared to the speed of light.

q We will learn only classical mechanics for two semesters.

n Modern physicsq deals with the relativity and quantum mechanics.

n The laws of physics can be used to predict the behaviourof the world and all kinds of machinery. Many of the everyday technological inventions that we now take for granted resulted from discoveries in physics. The basic laws in physics are universal, but physics in our time is such a vast field that many subfields are almost regarded as separate sciences.

3. Standards and Units

n  SI (Système International (french)) unit (or MKS unit) Time in s (second) Length in m (meter) Mass in kg

n  An equation must be dimensionally consistent (be sure you are adding apples to apples ).

n  Have no naked numbers (always use units in calculations).

Chapter 1Units, Physical Quantities, and Vectors

Length

n  Units q  SI – meter, m

n  Was: one ten-millionth of the distance from the North Pole to the equator

n  Now, defined in terms of a meter – the distance traveled by light in a vacuum during a given time

n  Speed of light is always the same in vacuum in any reference frame as 299 792 458 m/s

n  The distance traveled by light in vacuum during a time of 1/299 792 458 second.

Section 1.1

Time

n  Units q  seconds, s

n  Defined in terms of the oscillation of radiation from a cesium atom

n  One second is defined as 9 192 631 770 times the period of vibration of radiation from the cesium(Cs)-133 atom.

4. Uncertainty and Significant Figures

n  Significant figures : all the digits that are known accurately + one estimated digit

q  Digital meters

n  Rules q  Nonzero digits are always significant. q  Final or ending zeros to the right of the decimal point are

significant. q  Zeros written to the right of the decimal point for the purpose of

spacing the decimal point are not significant. q  Zeros written between significant figures are significant.

n  Examples q  409.9 s ( ), 0.058700 cm ( ), 9500 g ( ), 950.0×101 mL ( ) q  0.0001054 kg ( ), 0.005800 cm ( ), 602000 s ( )

n  When ambiguous, use the scientific notation.

n  Significant figures in calculations q  Addition, subtraction

q  Multiplication, division n  Round the answer to the shortest number of significant digits

in the numbers you are multiplying or dividing. n  28.84×6.2=4.651612 (in your calculator)

The answer should be _____________

7. Vectors and vector addition

n  A scalar quantity can be described by a single number. n  A vector quantity has both a magnitude and a direction in

space. n  A vector quantity is represented as .

n  The magnitude of is written as A or . A!"

A!"

|A!"|

n  Draw a vector as a line with an arrowhead at its tip. n  The length of the line shows the vector’s magnitude. n  The direction of the line shows the vector’s direction. n  A negative vector : a vector with same magnitude,

opposite direction. n  means they are antiparallel. !B = −

!A

8. Components of Vectors, Unit Vectors n  Vector Addition :

!C =!A+!B =!B +!A

Any of above three will work

§  Parallel vectors

commutative law

n  Addition of three or more vectors

n  Vector subtraction

!A

!B

!A−!B

à Draw a vector from B end to A end

n  If c is a scalar, the product has magnitude .

n  Multiplication of a vector

by a positive scalar and a negative scalar.

c!A |c |A

n  Components of Vectors (2-dimensional) q  Manipulating vectors graphically is insightful but difficult when

striving for numeric accuracy. Vector components provide a numeric method of representation.

q  Any vector is built from an x component and a y component. q  Any vector may be decomposed into its x component using Acos θ and its y component using Asin θ (where θ is the angle the vector A sweeps out from 0°).

A = Axî + Ay ĵ or

A = Ax , Ay= ( Ax , Ay )

Two ways to express a vector

The same vector may have different components depending on the choice of a coordinate.

n  In one coordinate system,

n  In another coordinate system

A = A

x

2 + Ay

2

θ = arctan

AyAx

= tan−1AyAx

tanθ =

AyAx

Ax = AcosθAy = Asinθ

Question types

1. Find a vector à Answer in vector form n  When expressing vectors in the physics class (exams),

use below method. q  Example) A vector with magnitude A=4.5 and angle β=36.9°.

q  Write down the answer using above form.

2. Find the magnitude and direction of a vector n  Express the magnitude in terms of a positive number,

direction in terms of angle measure from +x axis A= 3.25, θ = 126 from +x axis

A = Axî + Ay ĵ

!A = ( Ax , Ay )

n  Vector addition in component

Rx = Ax + Bx

Ry = Ay + By

R =A+B

!R =!A+!B +!C +!D +"

Rx = Ax + Bx + Cx + Dx +

Ry = Ay + By + Cy + Dy +

Unit vectors

n  Assume vectors of magnitude 1 with no units exist in each of the three standard dimensions.

n  The x direction is termed i, the y direction is termed j, and the z direction, k.

n  A vector is subsequently described by a scalar times each component.

A = Axî + Ay ĵ + Azk̂

n  Components of unit vectors

î = (1,0,0)ĵ = (0,1,0)k̂ = (0,0,1)

• Example 1) Find the angle between two vectors in the space.


10. Product of Vectors

n  Scalar Product (Dot Product) :

A ⋅B = Ax Bx + Ay By + Az Bz

A ⋅B = ABcosφ

A ⋅B

Examples) Work=

F ⋅ s

|A |2=

A ⋅A

⃗A = 2 ̂i + 3 ̂j + ̂k⃗B = − 4 ̂i + 2 ̂j − ̂k

n  Vector Product (Cross Product): !A×!B

A×B = −

B ×A

n  Vector product : magnitude

A×B = ABsinφ

Example) Torque=

r ×F

n  Vector product in vector notation :

n  For exact components, use determinant

î × ĵ = k̂ĵ × k̂ = îk̂ × î = ĵ

A×B =

î ĵ k̂Ax Ay AzBx By Bz

=

̂i × î = ĵ × ĵ = k̂ × k̂ =

n  Perpendicular or Parallel vectors

• Example 2) Vector ! has magnitude 6 units and is in the direction of the +x axis. Vector ! has magnitude 4 units and lies in the xy-plane, making an angle of 30° with +x axis. Find the vector product ! .

⃗A⃗B

⃗A × ⃗B