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# Classical mechanics

**Classical mechanics** is the part of physics that describes how everyday things move and how their motion changes because of forces. If we know how things are moving now, classical mechanics allows us to predict how they will move in the future and how they were moving in the past. We can use classical mechanics to predict how things like planets and rockets move.

There are two parts of mechanics. The two parts are classical mechanics and quantum mechanics. Classical mechanics is used most of the time for most of the things we can see, and that are not moving too fast. When the things are too small, classical mechanics is not good. Then we need to use quantum mechanics.

## Contents

## Newton's Three Laws

Newton's three laws of motion are important to classical mechanics. Isaac Newton discovered them. Newton's laws tell us how forces change how things move, but they do not say what causes the forces.

The *first law* says that if there is no external force (a push or pull), things that are not moving will stay not-moving, and things that are moving will keep moving in the same way. Before, people thought that things would slow down and stop moving even if there was no force making them stop. Newton said this was wrong. Often, people say, *Objects that are not moving tend to stay not-moving, and objects that are moving tend to stay moving, unless acted upon by an outside force, such as gravity, friction, etc...*

The *second law* says how much a force changes how a thing moves. When there is a net outside force on an object, its velocity (speed and direction of motion) will change. How fast the velocity changes is called the acceleration. Newton's second law says that bigger forces produce more acceleration. But objects with a lot of stuff in them (mass) are harder to push, so they do not accelerate as much. Another way of saying this is that the net force on an object equals the rate of change of its momentum. The momentum measures how much mass is in a thing, how fast it is going, and which direction it is going. So forces change the momentum, but how much they can change the speed and direction of motion still depends on mass.

The *third law* says that if one thing puts a force on another thing, the second thing also puts a force on the first thing. The second force is equal in size to the first force. The forces act in opposite directions. For example, if you jump forward off a boat, the boat moves backward. For you to jump forward, the boat had to push you forward. Newton's third law says that for the boat to push you forward, you had to push the boat backward. Often, people say, *For every action there is an equal and opposite reaction.*

## Kinematic Equations

In physics, kinematics is the part of classical mechanics that explains the movement of objects without looking at what causes the movement or what the movement affects.

### 1-Dimensional Kinematics

1-Dimensional (1D) Kinematics are used only when an object moves in one direction: either side to side (left to right) or up and down. There are equations with can be used to solve problems that have movement in only 1 dimension or direction. These equations come from the definitions of velocity, acceleration and distance.

- The first 1D kinematic equation deals with acceleration and velocity. If acceleration and velocity do not change. (Does not need include distance)
- Equation: [math]V_f=v_i+at[/math]
- V
_{f}is the final velocity. - v
_{i}is the starting or initial velocity - a is the acceleration
- t is time - how long the object was accelerated for.

- V

- Equation: [math]V_f=v_i+at[/math]
- The second 1D kinematic equation finds the distance moved, by using the average velocity and the time. (Does not need include acceleration)
- Equation: [math]x=((V_f+V_i)/2)t[/math]
- x is the distance moved.
- V
_{f}is the final velocity. - v
_{i}is the starting or initial velocity - t is time

- Equation: [math]x=((V_f+V_i)/2)t[/math]
- The third 1D kinematic equation finds the distance travelled, while the object is accelerating. It deals with velocity, acceleration, time and distance. (Does not need include final velocity)
- Equation: [math]X_f=x_i+v_it+(1/2)at^2[/math]
- [math]X_f[/math] is the final distance moved
- x
_{i}is the starting or initial distance - v
_{i}is the starting or initial velocity - a is the acceleration
- t is time

- Equation: [math]X_f=x_i+v_it+(1/2)at^2[/math]
- The fourth 1D kinematic equation finds the final velocity by using the initial velocity, acceleration and distance travelled. (Does not need include time)
- Equation: [math]V_f^2=v_i^2+2ax[/math]
- V
_{f}is the final velocity - v
_{i}is the starting or initial velocity - a is the acceleration
- x is the distance moved

- V

- Equation: [math]V_f^2=v_i^2+2ax[/math]

### 2-Dimensional Kinematics

2-Dimensional kinematics is used when motion happens in both the x-direction (left to right) and the y-direction (up and down). There are also equations for this type of kinematics. However, there are different equations for the x-direction and different equations for the y-direction. Galileo proved that the velocity in the x-direction does not change through the whole run. However, the y-direction is affected by the force of gravity, so the y-velocity does change during the run.

#### X-Direction Equations

*Left and Right movement*

- The first x-direction equation is the only one that is needed to solve problems, because the velocity in the x-direction stays the same.
- Equation: [math]X=V_x*t[/math]
- X is the distance moved in the x-direction
- V
_{x}is the velocity in the x-direction - t is time

- Equation: [math]X=V_x*t[/math]

#### Y-Direction Equations

*Up and Down movement. Affected by gravity or other external acceleration*

- The first y-direction equation is almost the same as the first 1-Dimensional kinematic equation except it deals with the changing y-velocity. It deals with a freely falling body while its being affected by gravity. (Distance is not needed)
- Equation: [math]V_fy=v_iy-gt[/math]
- V
_{fy}is the final y-velocity - v
_{iy}is the starting or initial y-velocity - g is the acceleration because of gravity which is 9.8 [math]m/s^2[/math] or 32 [math]ft/s^2[/math]
- t is time

- V

- Equation: [math]V_fy=v_iy-gt[/math]
- The second y-direction equation is used when the object is being affected by a separate acceleration, not by gravity. In this case, the y-component of the acceleration vector is needed. (Distance is not needed)
- Equation: [math]V_fy=v_iy+a_yt[/math]
- V
_{fy}is the final y-velocity - v
_{iy}is the starting or initial y-velocity - a
_{y}is the y-component of the acceleration vector - t is the time

- V

- Equation: [math]V_fy=v_iy+a_yt[/math]
- The third y-direction equation finds the distance moved in the y-direction by using the average y-velocity and the time. (Does not need acceleration of gravity or external acceration)
- Equation: [math]X_y=((V_fy+V_iy)/2)t[/math]
- X
_{y}is the distance moved in the y-direction - V
_{fy}is the final y-velocity - v
_{iy}is the starting or initial y-velocity - t is the time

- X

- Equation: [math]X_y=((V_fy+V_iy)/2)t[/math]
- The fourth y-direction equation deals with the distance moved in the y-direction while being affected by gravity. (Does not need final y-velocity)
- Equation: [math]X_fy=X_iy+v_iy-(1/2)gt^2[/math]
- [math]X_fy[/math] is the final distance moved in the y-direction
- x
_{iy}is the starting or initial distance in the y-direction - v
_{iy}is the starting or initial velocity in the y-direction - g is the acceleration of gravity which is 9.8 [math]m/s^2[/math] or 32 [math]ft/s^2[/math]
- t is time

- Equation: [math]X_fy=X_iy+v_iy-(1/2)gt^2[/math]
- The fifth y-direction equation deals with the distance moved in the y-direction while being affected by a different acceleration other than gravity. (Does not need final y-velocity)
- Equation: [math]X_fy=X_iy+v_iy+(1/2)a_yt^2[/math]
- [math]X_fy[/math] is the final distance moved in the y-direction
- x
_{iy}is the starting or initial distance in the y-direction - v
_{iy}is the starting or initial velocity in the y-direction - a
_{y}is the y-component of the acceleration vector - t is time

- Equation: [math]X_fy=X_iy+v_iy+(1/2)a_yt^2[/math]
- The sixth y-direction equation finds the final y-velocity while it is being affected by gravity over a certain distance. (Does not need time)
- Equation: [math]V_fy^2=V_iy^2-2gx_y[/math]
- V
_{fy}is the final velocity in the y-direction - V
_{iy}is the starting or initial velocity in the y-direction - g is the acceleration of gravity which is 9.8 [math]m/s^2[/math] or 32 [math]ft/s^2[/math]
- x
_{y}is the total distance moved in the y-direction

- V

- Equation: [math]V_fy^2=V_iy^2-2gx_y[/math]
- The seventh y-direction equation finds the final y-velocity while it is being affected by an acceleration other than gravity over a certain distance. (Does not need time)
- Equation: [math]V_fy^2=V_iy^2+2a_yx_y[/math]
- V
_{fy}is the final velocity in the y-direction - V
_{iy}is the starting or initial velocity in the y-direction - a
_{y}is the y-component of the acceleration vector - x
_{y}is the total distance moved in the y-direction

- V

- Equation: [math]V_fy^2=V_iy^2+2a_yx_y[/math]

## Related pages

## Other websites

- Science aid: Newton's laws of motion
- The Engineering Wiki's shorter page: Newton's laws of motion - engineers may improve it!
- Newtonian Physics - an on-line textbook
- Newtonian attraction for three Planets (Mathcad Application Server)
- Gravity - Newton's Law for Kids
- On Line Study Guide-study guide for high school students