Chapter 1: Introduction and Mathematical Concepts

**Physics**predicts how nature will behave in one situation based on the results of experimental data obtained in another situation.Physics is based on hypothesis testing through experimentation and observation.

Physics experiments involve a variety of measurements. Measurement should be accurate and reproducible.

Units of measurement:

Units for… | SI | Abbreviation |
---|---|---|

Length | Meter | m |

Mass | Kilogram | kg |

Time | Second | s |

Conversion units help us switch from one unit to another.

Examples:

Kilometers to meters

Grams to kilograms

Hours to seconds

Standard prefixes used to denote multiples of ten:

Prefix

Symbol

Factor

tera

T

10

^{12}giga

G

10

^{9}mega

M

10

^{6}kilo

k

10

^{3}hecto

h

10

^{2}deka

da

10

^{1}deci

d

10

^{-1}centi

c

10

^{-2}milli

m

10

^{-3}micro

$\mu$

10

^{-6}nano

n

10

^{-9}Pico

p

10

^{-12}femto

f

10

^{-15}

In all calculations, write down the units explicitly.

Treat all units as algebraic quantities. When identical units are divided, they are eliminated algebraically.

Use conversion factors in the text. Multiplying or dividing an equation by a factor of 1 does not altar the equation.

h is the hypotenuse, but can also be referred to as the resultant, R.

To find h, use the tangent equation.

A

**scalar**quantity is one that can be described by a single number.It gives a measurement.

Examples: temperature, speed, mass

A

**vector**quantity deals with inherently with both magnitude and direction.Examples: velocity, force, displacement

Arrows are used to represent vectors. The direction of the arrow gives the direction of the vector.

The length of a vector arrow is proportional to the magnitude of the vector.

Often it is necessary to add one vector to another.

“Resultant” = adding vectors together.

Examples:

**You must consider the signs**Case 1: Signs are both positive.

(+3.0 u) + (+2.0 u) = +5.0 u

Case 2: A is positive and B is negative

(+3.0 u) + (-2.0 u) = +1.0 u

**Consider directions**

x and y are called the x vector component and the y vector component of r.

To find x, y, or r, you can apply the sine, cosine, and tangent equations.

Vectors can broken down into several parts.

There can be several x and y components.

**Physics**is the branch of science that seeks to understand the fundamental principles governing the behavior of the universe.It is based on hypothesis testing through experimentation and observation.

Aims to describe and explain the interactions between matter, energy, space, and time.

Based on the fundamental assumption that the laws of nature are consistent and can be described mathematically.

The fundamental nature of physics lies in its pursuit of discovering the underlying principles and laws that govern the physical world.

Seeks to uncover the fundamental building blocks of matter and the forces that act upon them.

Physics encompasses a wide range of subfields, including:

Classical mechanics

Quantum mechanics

Electromagnetism

Thermodynamics

Relativity.

The discoveries and advancements in physics have led to numerous technological innovations and have impacted our understanding of the world around us.

Physics experiments involve measurements that should be accurate and reproducible.

The base units include:

Length (Mechanics)

Mass (Mechanics)

Time (Mechanics)

Temperature difference (Heat)

**Derived units**(or compound units) are all other quantities

**Newton (N)**- Force'Unit: $\dfrac{kg-m}{s^{2}}$

**Joules (J)**- EnergyUnit: $N-m$ or $\dfrac{kg-m^{2}}{s^{2}}$

When converting a large unit into a smaller unit, you move the decimal point to the

.__RIGHT__When converting a smaller unit into a larger unit, you move the decimal point to the

.__LEFT__Examples:

Example of scientific notation

All digits of a measured quantity are called

**significant figures**(SF).Rules of significant figures:

All non-zeros digits are significant.

**2**(2 SF)**453**(3 SF)**8493**(4 SF)

Zeros between nonzero digits of a number are significant.

**905**(3 SF)**7021**(4 SF)**10,632**(5 SF)

Zeros at the end of a number are significant if it contains a decimal point.

**450.**(3 SF)**12,000,000.**(8 SF)**130.0**(4 SF)

Zeros at the beginning of a number are

**NEVER**SIGNIFICANT.0.01 (1 SF)

0.00001 (1 SF)

A

**conversion factor**is a fraction that expresses one unit in terms of another that are equivalent to one another.Examples of conversion factors include:

1 meter = 100 centimeters

1 foot = 12 inches

1 meter = 39.37 inches

2.54 cm = 1 inch

1 mile = 5280 feet

1 yard = 36 inches = 3 feet

1000 meters = 1 kilometer

Equation for converting one unit into another:

To add or subtract two things, they must be in the

**SAME UNIT**In any equation, the physical dimensions of each term

**MUST BE IDENTICAL**

**Kinetic Energy** - Gravitational potential energy. Energy in motion.

m | mass | kg |
---|---|---|

v | velocity | m/s |

g | acceleration | m/s |

h | height | m |

J | energy | J |

**Kinetic energy formula**: $KE=\dfrac{1}{2}mv^{2}$**Potential energy formula:**$PE=mgh$

A

**scalar**quantity is one that can be described by a**single number**.It is a measurement.

Examples: temperature, speed, and mass.

A

**vector**quantity deals inherently with bothand__MAGNITUDE____DIRECTION__.Arrows represent them, the direction of the arrow gives the direction of the vector.

May point North, South, East, West, East of North, West of South, etc.

Examples: velocity, force, and displacement.

**Equation for Vector Addition**: $A+B=R$A + B represents distance traveled.

R represents displacement.

**If it is a triangle, you can use the equation**: $A^{2}+B^{2}=R^{2}$

**Physics**predicts how nature will behave in one situation based on the results of experimental data obtained in another situation.Physics is based on hypothesis testing through experimentation and observation.

Physics experiments involve a variety of measurements. Measurement should be accurate and reproducible.

Units of measurement:

Units for… | SI | Abbreviation |
---|---|---|

Length | Meter | m |

Mass | Kilogram | kg |

Time | Second | s |

Conversion units help us switch from one unit to another.

Examples:

Kilometers to meters

Grams to kilograms

Hours to seconds

Standard prefixes used to denote multiples of ten:

Prefix

Symbol

Factor

tera

T

10

^{12}giga

G

10

^{9}mega

M

10

^{6}kilo

k

10

^{3}hecto

h

10

^{2}deka

da

10

^{1}deci

d

10

^{-1}centi

c

10

^{-2}milli

m

10

^{-3}micro

$\mu$

10

^{-6}nano

n

10

^{-9}Pico

p

10

^{-12}femto

f

10

^{-15}

In all calculations, write down the units explicitly.

Treat all units as algebraic quantities. When identical units are divided, they are eliminated algebraically.

Use conversion factors in the text. Multiplying or dividing an equation by a factor of 1 does not altar the equation.

h is the hypotenuse, but can also be referred to as the resultant, R.

To find h, use the tangent equation.

A

**scalar**quantity is one that can be described by a single number.It gives a measurement.

Examples: temperature, speed, mass

A

**vector**quantity deals with inherently with both magnitude and direction.Examples: velocity, force, displacement

Arrows are used to represent vectors. The direction of the arrow gives the direction of the vector.

The length of a vector arrow is proportional to the magnitude of the vector.

Often it is necessary to add one vector to another.

“Resultant” = adding vectors together.

Examples:

**You must consider the signs**Case 1: Signs are both positive.

(+3.0 u) + (+2.0 u) = +5.0 u

Case 2: A is positive and B is negative

(+3.0 u) + (-2.0 u) = +1.0 u

**Consider directions**

x and y are called the x vector component and the y vector component of r.

To find x, y, or r, you can apply the sine, cosine, and tangent equations.

Vectors can broken down into several parts.

There can be several x and y components.

**Physics**is the branch of science that seeks to understand the fundamental principles governing the behavior of the universe.It is based on hypothesis testing through experimentation and observation.

Aims to describe and explain the interactions between matter, energy, space, and time.

Based on the fundamental assumption that the laws of nature are consistent and can be described mathematically.

The fundamental nature of physics lies in its pursuit of discovering the underlying principles and laws that govern the physical world.

Seeks to uncover the fundamental building blocks of matter and the forces that act upon them.

Physics encompasses a wide range of subfields, including:

Classical mechanics

Quantum mechanics

Electromagnetism

Thermodynamics

Relativity.

The discoveries and advancements in physics have led to numerous technological innovations and have impacted our understanding of the world around us.

Physics experiments involve measurements that should be accurate and reproducible.

The base units include:

Length (Mechanics)

Mass (Mechanics)

Time (Mechanics)

Temperature difference (Heat)

**Derived units**(or compound units) are all other quantities

**Newton (N)**- Force'Unit: $\dfrac{kg-m}{s^{2}}$

**Joules (J)**- EnergyUnit: $N-m$ or $\dfrac{kg-m^{2}}{s^{2}}$

When converting a large unit into a smaller unit, you move the decimal point to the

.__RIGHT__When converting a smaller unit into a larger unit, you move the decimal point to the

.__LEFT__Examples:

Example of scientific notation

All digits of a measured quantity are called

**significant figures**(SF).Rules of significant figures:

All non-zeros digits are significant.

**2**(2 SF)**453**(3 SF)**8493**(4 SF)

Zeros between nonzero digits of a number are significant.

**905**(3 SF)**7021**(4 SF)**10,632**(5 SF)

Zeros at the end of a number are significant if it contains a decimal point.

**450.**(3 SF)**12,000,000.**(8 SF)**130.0**(4 SF)

Zeros at the beginning of a number are

**NEVER**SIGNIFICANT.0.01 (1 SF)

0.00001 (1 SF)

A

**conversion factor**is a fraction that expresses one unit in terms of another that are equivalent to one another.Examples of conversion factors include:

1 meter = 100 centimeters

1 foot = 12 inches

1 meter = 39.37 inches

2.54 cm = 1 inch

1 mile = 5280 feet

1 yard = 36 inches = 3 feet

1000 meters = 1 kilometer

Equation for converting one unit into another:

To add or subtract two things, they must be in the

**SAME UNIT**In any equation, the physical dimensions of each term

**MUST BE IDENTICAL**

**Kinetic Energy** - Gravitational potential energy. Energy in motion.

m | mass | kg |
---|---|---|

v | velocity | m/s |

g | acceleration | m/s |

h | height | m |

J | energy | J |

**Kinetic energy formula**: $KE=\dfrac{1}{2}mv^{2}$**Potential energy formula:**$PE=mgh$

A

**scalar**quantity is one that can be described by a**single number**.It is a measurement.

Examples: temperature, speed, and mass.

A

**vector**quantity deals inherently with bothand__MAGNITUDE____DIRECTION__.Arrows represent them, the direction of the arrow gives the direction of the vector.

May point North, South, East, West, East of North, West of South, etc.

Examples: velocity, force, and displacement.

**Equation for Vector Addition**: $A+B=R$A + B represents distance traveled.

R represents displacement.

**If it is a triangle, you can use the equation**: $A^{2}+B^{2}=R^{2}$