# What is linear motion 1

## Movements in mechanics - physics for medical professionals

Table of Contents

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(An overview of all parameters can be found below.)

### Movements

### Uniform rectilinear movement

A uniform, straight movement is defined by a constant speed at which the direction does not change, which means that the same distances are covered at the same time intervals. The acceleration is zero here. This form of movement is described using the following formula:

v ⇒ web speed [m / s]

s ⇒ arc (corresponds to the path) [m]

t ⇒ time [s]

### Evenly accelerated movement

This form of movement is characterized by a changing speed. The moving object becomes faster or slower, from which it can be concluded that the acceleration here is not equal to zero. The acceleration a is constant during a uniformly accelerated movement. This movement is defined with **three laws**:

**Way-time law**

**Speed-time law**

a ⇒ acceleration [m / s^{2}]

v ⇒ web speed [m / s]

s ⇒ arc (corresponds to the path) [m]

t ⇒ time [s]

### Diagrams

The movements just described can be shown graphically in the following three diagrams. The uniform, straight-line movement is shown in red and the evenly accelerated movement is shown in green.

**Distance-time diagram**

**Speed-time diagram**

**Acceleration-time diagram**

### Freefall

The movement of free fall happens exclusively through the influence of gravity, which has an acceleration of a = g = 9.81 m / s. Free fall is a uniformly accelerated movement, because the acceleration due to gravity is constant. If one neglects the friction of the air and buoyancy, the following equations are obtained:g = 9.81 m / s

v ⇒ web speed [m / s]

s ⇒ arc (corresponds to the path) [m]

t ⇒ time [s]

h ⇒ height

### Uniform circular motion

The direction of this movement changes in the direction of a circle. Since the velocity is a vector, the different directions of the velocity would cancel each other out. Therefore the uniform circular motion is defined with the constant amount of the speed. Or to put it simply: if you drive your car in a circle and set the cruise control to 50 km / h, your acceleration will be constant and will not change. But their direction is constantly changing.

ω ⇒ angular velocity [1 / s]

α ⇒ angular acceleration [1 / s^{2}]

a ⇒ acceleration [m / s^{2}]

v ⇒ web speed [m / s]

s ⇒ arc (corresponds to the path) [m]

t ⇒ time [s]

n ⇒ speed [1 / s]

r ⇒ radius

π ⇒ circle number (around 3.14)

### Periodic movements

Periodic movements are temporal changes in a system or a physical variable around a position of rest, in which every occurring state of movement is repeated approximately or exactly after a period and is defined as follows.

T ⇒ period in seconds [s]

f ⇒ frequency in Hertz [Hz]

ω ⇒ angular velocity [1 / s]

### Momentum and force

### Newton's axioms

**Axiom I: equilibrium condition**

A body remains in a state of rest or uniform translation, as long as it is not forced to change its state by acting forces.

This means that under the conditions mentioned, the speed of a body is constant and can only be changed by the action of a force.

**Axiom II: Basic Equation of Mechanics**

The change in movement is proportional to the action of the moving force and takes place in the direction of the straight line in which that force acts.

**Axiom III: Counteraction Principle**

Forces always appear in pairs. If a body A exerts a force on another body B (actio), an equally large but opposing force from body B acts on body A (reaction).

Action = reaction

### pulse

The momentum is a directed quantity, the direction of which is parallel to the movement of a body and describes the mechanical state of movement of this body.

p ⇒ impulse [kg * m / s], [N * s]

m ⇒ mass [kg]

### Conservation of momentum

The law of conservation of momentum describes that all momentum within a closed system, which therefore does not interact with its environment, is constant. The impulses of two balls hitting against each other must therefore be the same before and after the impact.

### Powers

Forces deform bodies, set them in motion or accelerate them. So the force is a performing work in which the energy of the body changes. The general equation of force is defined as follows:

F ⇒ force 5812, [kg * m / s^{2}]

m ⇒ mass [kg]

a ⇒ acceleration [m / s^{2}]

There are different forms of forces, which are represented in the following equations:

force | equation | description |

Weight force F_{G} | Plumb (downward) force acting due to gravity. The acceleration due to gravity g is a firmly defined value: g = 9.81 m / s^{2} | |

Buoyancy force F_{A.}swim Sink Climb | Buoyancy in liquids; ρ_{Fl =}Density of the liquid [kg / m³]; V = volume of the body which is in the liquid [m³] | |

Spring force | Deflection of a spring D; Spring constant (material-specific constant) [N / m]; ∆L = length / extension of the spring [m] | |

Normal force | Force acting perpendicular to the support surface of a body. In a horizontal plane, the normal force is equal to the weight. α = angle of the normal force to the perpendicular | |

Tangential force | Force acting parallel to the contact surface of the body | |

Static friction | Force that counteracts a movement of a body. Depending on the material and surface properties of the bodies that are in contact; μ_{H} = Coefficient of static friction, without a unit | |

Sliding friction force | Opposite force of two "sliding" bodies on each other; μ_{G} = Coefficient of sliding friction, without units | |

Rolling friction force | Force required to set a rolling body in motion; μ_{Roll} = Coefficient of rolling friction, without units. The use of lubricants reduces the coefficient of friction. Accordingly, less force is required to create a movement between two bodies rubbing against one another. | |

Centrifugal force | Force directed outward from the center of the circle by the inertia of a spinning body. r = circle radius [m]; M = mass of the body; ω = angular velocity [1 / s] | |

Centripetal force | Force acting from the outer circumference of a circle to the center, opposite to the centrifugal force. | |

Coulomb force | Describes how strongly two bodies or particles attract each other. Depending on the strength of the charge and the distance of the bodies / particles; ε_{0} = Electric field constant; ε_{r} = Dielectric constant; Q1, Q2 charges of the two bodies [C]; r = distance from the center of the two bodies |

### Impulse

The impulse of force is defined as the temporal change in the momentum caused by an average force, which is defined as:

I.^{→ }⇒ impulse [kg * m / s]

F._{av} ⇒ Average force 5812, [kg * m / s2]

p ⇒ momentum

Δt ⇒ duration of the shock

### Torque, moment of inertia, angular momentum

### Center of mass

The geometric center point does not always correspond to the center of mass, since the influence of density (i.e. the influence of the mass of a body) plays a decisive role in the latter. It is defined as the center of gravity of a system of any number of mass points A._{0}, A_{1}, A_{2}… A_{n}that have the same mass:

M._{S.} Center of mass, without units

The weight acts on the center of mass (also called the center of gravity). The center of gravity of the human body is, for example, in the hip area when standing firmly. However, the center point varies depending on the movement and posture and can even be outside the body in extreme movement situations.

The position of the body's center of gravity determines the equilibrium we are in. A distinction is made here:

- Stable equilibrium: the body returns to its original position after a deflection.
- Unstable equilibrium: After a deflection, the body that was previously in equilibrium will move further away from it.
- Indifferent balance: the body assumes a new weight position.

### Torque

The torque causes a body to rotate around an axis of rotation. It depends on the distance between the axis of rotation and the point of application of the force. Force times force arm is equal to load times load arm. The following definition describes the torque:

M ⇒ torque [N * m]

**Example:**Muscles act on joints, which - from a physical point of view - are the axes of rotation. These generate a torque with the application of force.

### Moment of inertia

A static / rigid body has a resistance. If this body is set in a rotational movement by a force, a moment of inertia arises which is mainly dependent on the mass distribution of the body in relation to the axis of rotation.

J ⇒ moment of inertia [kg * m^{2}]

r ⇒ axis of rotation

ρ ⇒ mass distribution

### Angular momentum

The angular momentum is also known colloquially as twist or momentum. It indicates the direction and momentum of a turn around an axis and becomes larger:

- the greater the mass of the body.
- the higher the speed of the body.
- the greater the distance to the axis of rotation.

It is defined with the following formula:

### job

W ⇒ work [J], [N * m]

Through work, energy is transferred from one body to another. As a result, it can either be moved or deformed. As with strength, there are different forms of work, which are explained in more detail below.

job | equation | description |

Lifting work | Lifting a body; h = height that the body is excavated | |

Acceleration work | Acceleration of a body by going faster or slower; s = path; F._{B.} = Acceleration force | |

Pressure-volume work | The volume of a fluid is reduced by compression (V2 |

### energy

E ⇒ energy [J], [N * m]

Energy is a fundamental part of life because it ensures that life exists, that objects are moved against a force, pressure is exerted, substances are heated, pressure exerted, substances are heated or electrical current is allowed to flow. The two main forms of energy are described as follows:

energy | equation | description |

Potential energy | Positional energy, e.g. energy that a body of a certain mass has at a known altitude; h = height above the ground | |

Kinetic energy | Kinetic or acceleration energy; an object is set in motion out of rest | |

Pressure-volume work | The volume of a fluid is reduced by compression (V2 |

### Conservation of energy law

Since it is not possible to generate or destroy energy, the energy in a closed system is always constant. Energy loss only occurs because the energy supplied can be converted (kinetic energy into thermal energy) or given off (in the form of heat radiation). The definition of a closed system plays a major role here and may only be named as such without the exchange of energy, information or substances and without any interaction with the environment.

### power

P ⇒ power [W], [J / s]

The performance describes how much energy is converted in a certain period of time and is therefore dependent on the time. The work done or the energy supplied is inversely proportional to time. This means that the power will decrease over time at a constant energy.

### Central thrust

Δp ⇒ shock [(kg * m) / s]

A shock is defined as a change in momentum over time and is described by the following equation:

There are two types of impact:

- Elastic collision: conservation of kinetic energy
- Inelastic collision: conversion of part of the kinetic energy into internal energy

Collisions involving two bodies whose centers of gravity move in a straight line are known as central impacts.

The pressure is measured using a so-called manometer. The pressure is the result of a force that acts on a surface:

p ⇒ pressure [Pa], [N / m^{2}]

A ⇒ area [m^{2}]

V ⇒ volume [m^{3}], [l]

### Boyle Puppet Law

The Boyle-Marionette Law applies to ideal gases and states that these react indirectly proportionally with a change in volume when there is a change in pressure. For example, if you let half the volume out of a compressed air cylinder, then the pressure in the cylinder is only about half as high. It can also be described with the following formula:

### Overview of the parameters

t or t_{0} | Time [s] |

v or v_{0} | Speed [m / s] |

s or s_{0} | Way [m] |

a | Acceleration [m / s^{2}] |

g = 9.81 m / s^{2} | Acceleration due to gravity [m / s^{2}] |

H | Height or height of fall [m] |

α | Angular acceleration [1 / s^{2}] |

s | Arch (corresponds to the path) [m] |

r | Radius [m] |

n | Speed [1 / s] |

v | Web speed [m / s] |

T | Period in seconds [s] |

f | Frequency in Hertz [Hz] |

ω | Angular frequency in one per second [1 / s] (angular velocity) |

Φ | Angle that is exceeded |

p | Impulse [kg * m / s], [N * s] |

m | Mass [kg] |

F. | Force 5812, [kg * m / s^{2}] |

I → | Impact [kg * m / s] |

F._{av} | Average force 5812, [kg * m / s^{2}] |

M._{s} | Center of mass, without units |

M. | Torque [N * m] |

J | Moment of inertia [kg * m^{2}] |

r | Axis of rotation |

ρ | Mass distribution |

L. | Angular momentum [(kg * m^{2}) / s] |

p | Impulse of the mass point [(kg * m) / s] |

W. | Work (J), [N * m] |

E. | Energy [J], [N * m] |

P. | Power [W], [J / s] |

Δp | Shock [(kg * m) / s] |

ρ | Pressure [Pa], [N / m^{2}] |

A. | Area [m^{2}] |

V. | Volume [m^{3}], [l] |

### Popular mechanics exam questions

The solutions can be found below the references.

1. A body made of platinum is immersed in a mercury bath, a second made of aluminum in a water bath. Both are connected to one another with a thread via pulleys. In equilibrium, the platinum is completely immersed, while the aluminum body remains with half of its volume above the surface of the water.

Densities:

Platinum: 21.5 g / cm³

Mercury 13.6 g / cm³

Aluminum: 2.7 g / cm³**What is the value of the volume (aluminum body) / volume (platinum body) ratio?**

- 8
- 4,6
- 9,3
- 3,6
- 18

**2. A spring is stretched by 50 mm by an attached weight G1. An additional weight G2 with a mass of 30 g expands the spring by an additional 36 mm.****With what force does G1 pull on the spring?**

- 0.4 N
- 72 g
- 0.3 N
- 0.7 N
- 42 g

**3. Which of the following statements is / are wrong?**

- In the case of a uniformly accelerated movement (example: free fall), the acceleration increases linearly with time.
- When the acceleration is zero, the speed is also zero.
- If the magnitude of the speed is constant, the acceleration is always zero.
- If a body is accelerated perpendicular to its direction of movement - with a constant amount of acceleration - the result is always a circular path.

- Just b, c, d
- Just c
- Just a
- All except d
- All

### swell

Romberg, Hinrichs: Do not panic about mechanics; Vieweg-Teubner-Verlag; 8th edition, 1999

Hut: basics of engineering; Springer Verlag, 29th edition, 1989

Physics - formulas and laws; Paperback publisher

Linder: physical tasks; Fachbuchverlag Leipzig-Cologne, 1992

http://www.ubicampus.mh-hannover.de/~fahlke/MC/mc1.pdf

**Solutions to the questions:** 1D, 2A, 3E

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