# TFY4125: Fysikk

# The exam

The exam consists of a 30 questions-long MCQ. It is worth noting that you do **not** need to learn every formula here, but at least know what they correspond to, as most of them are given in the formula sheet at the exam. Below is a rough count of the amount of questions asked about varous themes these last 4 years.

The general conclusion is as follows:

- The exam covers most of the curriculum
- Learn your Motions
- Learn your Rotational motions
- Learn your periodic motion
- Read everything from Thermodynamics
- Read everything from Electromagnetism
- Do the past exams: several questions are recycled from year to year

# Units

Three fundamental physical quantities are mass, length, and time. The corresponding fundamental SI units are the kilogram, the meter, and the second. Derived units for other physical quantities are products or quotients of the basic units. Equations must be dimensionally consistent; two terms can be added only when they have the same units.

Since the exam is an MCQ, it can sometimes be easier to analyse the units involved than to actually solve a problem. Here is a table summarising various SI units and their definition with basis units (if appliable).

Measure |
SI unit |
Definition |

Mass (m) | kilogram (kg) | - |

Length (l) | meter (m) | - |

Time (t) | second (s) | - |

Temperature (T) | Kelvin (K) | °C + 273.15 |

Electric current (I) | Ampere (A) | |

Amount of substance | mole (mol) | - |

Acceleration (a) | - | |

Velocity (v) | - | |

Force (F), Weight | Newton (N) | |

Work (w) | Joule (J) | |

Pressure (p) | Pascal (Pa) | |

Capacitance (C) | Farad (F) | |

Electric charge (Q) | Coulomb (C) |

# Significant values

The accuracy of a measurement can be indicated by the number of significant figures or by stated uncertainty. The significant figures in the result of a calculation are determined by the following rules:

- Multiplication and division
- Result can have no more significant figures than
*the factor with the fewest significant figures*. For example: (0.745 x**2.2**)/3.885 = 0.42 - Addition or subtraction
- Number of significant figures is determined by
*the term with the largest uncertainty (i.e., fewest digits to the right of the decimal point)*. For example: 27.153 +**138.2**- 11.74 = 153.6.

When only crude estimates are available for input data, we can often make useful order of magnitude estimates.

# Mechanics

## A small reminder about vectors

## Motion along a straight line

Average velocity:

Instantaneous velocity:

Average acceleration:

Instantaneous acceleration:

### Straight-line motion with constant acceleration

### Straight-line motion with variable acceleration

### Freely falling bodies

Free fall is a case of motion with constant acceleration. The magnitude of the acceleration due to gravity is a positive quantity, g. The acceleration of a body in free fall is always downward.

## Motion in 2D and 3D

Not much difference from 1D, except we decompose the movement into x, y and z components.

### Projectile motion (2D)

Assuming we have no air resistance, we get:

To find the maximum height of the movement, set

To find the range of the movement, set

### Uniform and nonuniform circular motion

**(Needs verification)** *The 'rad' subscript denotes that the acceleration always lies on top of the radius (meaning always pointing to the center)*

**(Needs verification)** *The 'tan' subscript denotes the tangent acceleration.
If an object moving in a circle is speeding up/slowing down, we can decompose the acceleration into two perpendicular vectors; radius and tangent ( $a_{rad}$, $a_{tan}$)*

## Forces and Newton's laws

### Weight

### Newton's first law

Newton's first law can be stated as: "A body will keep doing what it is doing as long as the sum of the forces acting on it is equal to 0".
Or mathematically:

### Newton's second law

Newton's second law tells us what happens when the sum of the forces acting on a body is not equal to 0. Mathematically:

### Newton's third law

Newton's third law states that when a body A exerts a force on another body B, then B will exert a force of equal magnitude in the opposite direction. Or mathematically:

### Normal force

The normal force is the force that acts on a body resting on a surface, perpandicular to the surface. The normal force is expressed by:

### Friction

There are 2 types of friction: kinetic friction and static friction. Kinetic friction is the force that acts on a body that slides on a surface, and its magnitude is given by:

Static friction on the other hand is the force that acts on a body that is not moving on a surface. Its magnitude is anywhere between 0 and its maximum, which is given by:

The direction of the friction's force vector is in the opposite direction of the movement of the body (essentially "slowing" the body).

### Air resistance

A decent approximation of the effects of air resistance is given by

An object in free fall reaches terminal velocity when its air resistance is equal to the gravitational force acting on it, and hence its acceleration becomes

### Pulleys

In a system with 1 pulley with 2 masses

### Centripetal force

The centripetal force is the force necessary to keep an object in circular motion. Its value is

### Spring force

The force needed to compress or extend a spring by a distance x is given by

## Work and kinetic energy

### Work done by a constant force

A force does work if it produces a displacement. Note that work is a scalar quantity and not a vector. It is defined by:

### Work done by a varying force

When the applied force varies and can be expressed by a function

### Kinetic energy

The kinetic energy of a particle is the amount of work needed to accelerate the particle from rest to a speed

The total amount of work done on a particule is equal to the change of kinetic energy it experiences when going from a speed

### Power

Power is the time rate of doing energy. It is a scalar like work and kinetic energy. The average power is given by:

## Potential energy and energy conservation

### Gravitational potential energy

The gravitational potential energy is the energy stored in an object due to its height. It is given by

### Elastic potential energy

The elastic potential energy is the energy stored in an elastic object due to its stretching or compressing. It is given (in the case of an ideal spring following Hooke's law) by

### Mechanical energy

The total mechanical energy is given by

#### Conservative total mechanical energy

If no forces other than the elastic and gravitational potential energies do work on an object, then we have

#### Non-conservative total mechanical energy

If other forces do work as well on an object, then we have

### The law of conservation of energy

A force is either conservative or nonconservative. It is nonconservative if its work depends on other factors than kinetic and potential energy, for instance if the path taken affects its work: an example of this is the friction force. However, the following law holds for all forces

## Momentum, Impulse and Collisions

### Momentum

The momentum of an object refers to the quantity of motion that it has, and is given by

### Impulse

Impulse describes the change in momentum, given by

### Conservation of momentum:

As long as the only forces acting on a system are the forces internal to the system, the total momentum of the system (the sum of all momenta in the system) is constant.

### Collision

#### Elastic collision

An elastic collision is a collision in which there occurs no loss of kinetic due to the collision (no friction...). If we have 2 objects A and B colliding with initial velocity

#### Inelastic collision

An inelastic collision is a collision in which there is a loss of kinetic energy.

### Center of mass

The center of mass of a body may be found by computing the weighted position of the various masses and dividing by the sum of the masses. Mathematically, the position of the center of mass in centimeters

## Rotation of rigid bodies

### Rotational kinematics

Given a rigid body rotating about a stationary axis z, then the body's position is described by the angular coordinate

### Relating linear and angular kinematics

Given an object travelling at a distance

### Moment of inertia and rotational kinetic energy

The moment of inertia of a body about an axis is a measure of its rotational inertia and is given by

## Dynamics of rotational motion

### Torque

Torque is a measure of the force that causes an object to acquire angular acceleration. It is given by

### Rotational dynamics

The rotational equivalent of Newton's second law states that

### Combined translation and rotation

In the case that a body is moving as well as rotating, we may express its kinetic energy as

If a body is made to rotate about an axis that is parallel to the old rotation axis, and at a distance

### Work done by a torque

The work resultant of a torque that acts on a rotating body is given by

### Angular momentum

The angular momentum of a particle is given by

### Rotational dynamics and angular momentum

We may combine our previous discussions in order to conclude that the sum of external torques on the system is equal to the rate of change of the total angular momentum of the system, or

## Equilibrium and elasticity

A rigid body is in equilibrium if

Stress (force per unit area) divided by strain (fractional deformation) is equal to the elastic modulus.
A body is elastic if it returns to its initial state after the stress is removed. Otherwise, the body is plastic. If we apply a force

## Pressure in a fluid

The pressure difference

### Pascal's Law

Pressure applied to an enclosed fluid is transmitte undiminished to every portion of the fluid and the walls of the containing vessel.

## Periodic motion

### Oscillation

Period

### Simple harmonic motion

Simple harmonic motion (SHM) occurs when the oscilation does not change, for example when a spring obeys Hooke's law. We can define the restoring force exerted by an ideal spring in this case with

### Simple pendulum

If there is a small amplitude, we have

### Damped oscillations

If there is a little damping, we get

### Forced oscillation

The amplitude of a forced oscillator may be described by

# Thermodynamics

## Temperature and heat

The Kelvin temperature scale is defined by the ratio of 2 temperatures in kelvins

### Thermal expansion

The length

### Quantity of heat

The **calorie** is the amount of heat required to raise the temperature of 1 gram of water from 14.5°C to 15.5°C.

### Calorimetry and phase changes

A phase is a specific state of matter.
The heat stransfer in a phase change is given by

### Mechanisms of heat transfer

**Conduction** is the transfer of heat within materials bulk motion of the materials. Its heat current is given by

**Convection** is complex.

**Radiation** is the transfer of heat by electromagnetic waves. Its heat current is given by

## Thermal properties of matter

### Equations of state

In order to "weight" a gas, we may use the following equation: **ideal gas** is a gas for which the following equation holds for all pressures and temperatures:

### Molecular properties of matter

A

moleis the amount of substance that contains as many elementary entities as there are atoms in 0.012 kilogram of carbon-12.

The molar mass

## The first law of thermodynamics

The first law of thermodynamics is defined by

### Work done during volume changes

When a gas changes volume, it produces work defined by

### Paths between thermodynamic states

There are several ways for a thermodynamic system to progress from an initial state to a final state, and during this progress the system passes through a series of intermediate states, which we refer to as a **path**.

### Internal energy

The internal energy of any thermodynamic system depends only on its state. The change in internal energy in any process depends only on the initial and final states, not on the path. The internal energy of an isolated system is constant.

### Kinds of thermodynamic processes

An **adiabatic process** is a process in which there is no heat transfer in and out of the system, ie.

In an **isochoric process**, the volume is constant, ie.

In an **isobaric process**, the pressure is constant, ie.

In an **isothermal process**, the temperature is constant.

### Ideal gases

The internal energy U of an ideal gas depends only on its temperature T, not on its pressure or volume.

We have the following definition for the molar heat capacity

## The second law of thermodynamics

An **irreverseible** thermodynamic process is one that occurs spontaneously in one direction but not the other. A **reversible** thermodynamic process is a process that can be reversed by applying infinitesimal changes; the system is hence almost always in equilibrium.

The second law of thermodynamics may be defined in several ways. Engine statement:

It is impossible for any system to undergo a process in which it absorbs heat from a reservoir at a single temperature and converts the heat completely into mechanical work, with the system ending in the same state in which it began.

Refrigeration statement:

It is impossible for any process to have as its sole result the transfer of heat from a cooler to a hotter body.

Entropy statement:

The entropy of an isolated system may increase but can never decrease.

### Engines

A heat engine converts heat

If an engine uses an Otto cycle, its thermal efficiency is

The **Carnot cycle** is a hypothetical engine that yields the maximum possible efficiency without breaking the second law of thermodynamics. It consists of only reversible processes. Its efficiency is

### Refrigerators

A refrigirator is essentially a reverse heat engine. Given

### Entropy

Entropy is a measurment of randomness of a system. In a reversible process, entropy change is defined by

# Electromagnetism

## Electric charge and electric field

The algebraic sum of all the electric charges in any closed system is constant.

Coulomb's law:

The magnitude of the electric force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance

$r$ between them:$F = k\frac{|q_1q_2|}{r^2}.$

Usually,

The electric field is defnied by

## Electric potential

The electric force caused by any collection of charges at rest is a conservative force. Hence we can express the work done by

The electric potential due to a point charge is

If the potential

## Capacitance and dielectrics

The capacitance of a capacitor (in farad) is given by

The potential energy stored in a capacitor is

**Energy density** is the energy per unit volume in the space between the plates of a parallel-plate capacitor in vacuum, and is given by