# What is the motion of inertia

## Movement through strength and energy

### The classical (Newtonian) mechanics

**Isaac Newton** was the founder of **classical mechanics**, hence also called Newtonian mechanics. He dealt with that **Rigid body dynamics**So he was investigating the effect of forces on the **State of motion** of *non-deformable bodies and mass points*. From his observations he deduced three **Newton's laws** or. **Newton's axioms**that are still valid today for everyday problems.

Despite complicated theories such as general relativity, simple Newtonian mechanics is sufficient to describe the vast majority of gravitational phenomena such as planetary or satellite orbits.

### Mass points and center of gravity

Every spatially extended body can be described in physics as a dimensionless one **Ground point** describe the same mass. When a force acts on a body, it actually acts on each of them *many small particles*that make up a body. But since that would be too time-consuming to calculate, the forces of all particles are replaced by the **resulting power** at the **main emphasis** of the body. The center of gravity has no spatial expansion and unites the entire mass. The position of the center of gravity also determines the **Stability and balance** of an object.

### Newton's 1st axiom - principle of inertia

The **1. Newton's law** describes the *Sluggishness of a body* and will therefore also **Principle of inertia** called. The law says that a body is in his *State of motion persists*, provided *no external force* works. The reverse consequence of the law says that the sum of all external forces is zero if a body is at rest or moves at constant speed (uniform movement).

### Examples - principle of inertia

You can experience for yourself what inertia means every time you drive a car: If the car drives around a curve or brakes, you will be pressed into the seat belt. Your body is *sluggish*, that is, he wants to maintain his state of motion (driving at a constant speed in a certain direction). By braking or steering, the car exerts a force on you that the *Direction or speed* your movement changes. The **Centrifugal force**that presses you into the belt in a curve is therefore only one **Sham power**caused by the **Inertia of the crowd**.

An example of that *Reversal of the Law* is the ride with *constant speed*. Two forces act here, the propelling force of the engine and the friction between the road and the tires acting in the opposite direction. If these forces balance each other out exactly (sum of the forces equals zero), the car drives consistently fast.

### Newton's 2nd axiom - principle of action

The **2. Newton's law** or **Principle of action** is an equation of motion and the **Basic equation of dynamics**. It says that an external force is one *Change of momentum* entails.

$ \ vec {F} = \ dot {\ vec {p}} $

The momentum is the product of mass and speed: $ \ vec {p} = m \ vec {v} $. This results in problems for most of the *constant mass* the familiar formula

$ \ vec {F} = m \ dot {\ vec {v}} = m \ vec {a} $.

A body, on which the force $ F $ acts, experiences an acceleration $ a $ in the same direction. The **inert mass** $ m $ is a type *Resistance to the force* and can be understood as a measure of the inertia of a body. In the event that no external force acts ($ F = 0 $), the body does not experience any change in speed ($ a = 0 $). This is precisely the statement of the 1st axiom.

This means that the knowledge of all acting forces, the starting point and the starting speed is sufficient to determine the location and the speed *any time* $ t $.

### Examples - principle of action

With the same engine power ($ F $), a loaded car takes longer to accelerate from 0 km / h to 100 km / h ($ a $) than an empty car, because its mass $ m $ is greater.

The speed $ v $ is one **vectorial size**, that is, she has one **amount** and a **direction**. If you spin a body on a rope in circular movements through the air, you are practicing one **centripetal force** along the rope. The acceleration that a body after **2nd axiom** must experience, is expressed not in the change in the amount of the speed, but in the constant *Change of direction*. If the force is no longer effective (letting go of the rope), the body flies **tangential** from that.

### Radial force and radial acceleration

Newton's 2nd axiom also applies to **Circular movements**. A body on a circular path, like the body on a rope, the satellite orbiting the earth or the earth orbiting the sun, experiences one **Radial force and radial acceleration**. The radial force or **centripetal force** is

$ F = \ frac {mv ^ 2} {r} $

and shows *perpendicular* to the direction of movement towards the center of the circle. In the satellite example, the gravitational force is the centripetal force. The **Tangential velocity** remains constant despite the force acting. But this is not a contradiction to the 2nd axiom, since instead the direction of the tangential velocity changes.

### Newton's 3rd axiom - interaction principle

With the **Conservation of momentum** it can be deduced that the force exerted by the *Body 1* on the *Body 2* is performed, *the same amount* the force is that of *Body 2* on *Body 1* is performed. The direction of the force is *contrary*. this is that **3. Newton's axiom** or **Interaction principle**, also **Actio and Reactio** called.

$ \ vec {F_ {12}} = - \ vec {F_ {21}} $

### Examples - principle of interaction

The **Gravitational pull of the earth** on you is just as great as the attraction you exert on the earth. The difference is the different **Dimensions** and hence indolence of the body. Since you oppose the force with a significantly smaller mass than the earth, you will be accelerated much more towards earth than the other way around. After this **Equivalence principle** corresponds to the heavy mass that is the cause of gravity ($ F = mg $), the inert mass that counteracts an external force ($ F = ma $).

The principle of **Actio and Reactio** you can try it out for yourself: you and a friend with **same** Body weights face each other on a skateboard. You hold a rope in your hands. If you pull on the rope, your friend has to exert exactly the same amount of force to hold the rope in his hands. You will both move towards each other and meet in the middle, although only you have "pulled" the rope.

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