# TFY4125: Fysikk

# 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) |

# Mechanics

Noen ta i et tak her, og ikke vær like lat som meg å lim inn bilder fra sammendraget i boka

## 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

## Motion in 2D and 3D

Not much difference from 1D, expect 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

## 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 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

## 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