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 a 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 (
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:
Molecular properties of matter
A mole is 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