Classical mechanics

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Mechanics is a part of physics. It says what happens when forces act on things. 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. Some of the time, for example when the things are too small, classical mechanics is not good. Then we need to use quantum mechanics.

Newton's Three Laws

File:Newtons laws in latin.jpg
A page from Newton's book about the three laws of motion

Newton's three laws of motion are important to classical mechanics. Isaac Newton made them.

The first law says that, if there is no external force (meaning there is no pushing, gravity, or any sort of power), things that are stopped will stay stopped or un-moving, and things that are moving will keep moving. Before, people thought that things stopped if there was no force present. Often, people say, Objects that are stopped tend to stay stopped, 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 a force moves a thing. The net force on an object equals the rate of change of its momentum.

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. 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.

  1. The first 1D kinematic equation deals with acceleration and velocity. If acceleration and velocity do not change. (Does not need include distance)
    Equation: [math]\displaystyle{ V_f=v_i+at }[/math]
    Vf is the final velocity.
    vi is the starting or initial velocity
    a is the acceleration
    t is time - how long the object was accelerated for.
  2. The second 1D kinematic equation finds the distance moved, by using the average velocity and the time. (Does not need include acceleration)
    Equation: [math]\displaystyle{ x=((V_f+V_i)/2)t }[/math]
    x is the distance moved.
    Vf is the final velocity.
    vi is the starting or initial velocity
    t is time
  3. 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]\displaystyle{ X_f=x_i+v_it+(1/2)at^2 }[/math]
    [math]\displaystyle{ X_f }[/math] is the final distance moved
    xi is the starting or initial distance
    vi is the starting or initial velocity
    a is the acceleration
    t is time
  4. 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]\displaystyle{ V_f^2=v_i^2+2ax }[/math]
    Vf is the final velocity
    vi is the starting or initial velocity
    a is the acceleration
    x is the distance moved

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
  1. 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]\displaystyle{ X=V_x*t }[/math]
    X is the distance moved in the x-direction
    Vx is the velocity in the x-direction
    t is time

Y-Direction Equations

Up and Down movement. Affected by gravity or other external acceleration
  1. 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]\displaystyle{ V_fy=v_iy-gt }[/math]
    Vfy is the final y-velocity
    viy is the starting or initial y-velocity
    g is the acceleration because of gravity which is 9.8 [math]\displaystyle{ m/s^2 }[/math] or 32 [math]\displaystyle{ ft/s^2 }[/math]
    t is time
  2. 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]\displaystyle{ V_fy=v_iy+a_yt }[/math]
    Vfy is the final y-velocity
    viy is the starting or initial y-velocity
    ay is the y-component of the acceleration vector
    t is the time
  3. 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]\displaystyle{ X_y=((V_fy+V_iy)/2)t }[/math]
    Xy is the distance moved in the y-direction
    Vfy is the final y-velocity
    viy is the starting or initial y-velocity
    t is the time
  4. 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]\displaystyle{ X_fy=X_iy+v_iy-(1/2)gt^2 }[/math]
    [math]\displaystyle{ X_fy }[/math] is the final distance moved in the y-direction
    xiy is the starting or initial distance in the y-direction
    viy is the starting or initial velocity in the y-direction
    g is the acceleration of gravity which is 9.8 [math]\displaystyle{ m/s^2 }[/math] or 32 [math]\displaystyle{ ft/s^2 }[/math]
    t is time
  5. 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]\displaystyle{ X_fy=X_iy+v_iy+(1/2)a_yt^2 }[/math]
    [math]\displaystyle{ X_fy }[/math] is the final distance moved in the y-direction
    xiy is the starting or initial distance in the y-direction
    viy is the starting or initial velocity in the y-direction
    ay is the y-component of the acceleration vector
    t is time
  6. 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]\displaystyle{ V_fy^2=V_iy^2-2gx_y }[/math]
    Vfy is the final velocity in the y-direction
    Viy is the starting or initial velocity in the y-direction
    g is the acceleration of gravity which is 9.8 [math]\displaystyle{ m/s^2 }[/math] or 32 [math]\displaystyle{ ft/s^2 }[/math]
    xy is the total distance moved in the y-direction
  7. 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]\displaystyle{ V_fy^2=V_iy^2+2a_yx_y }[/math]
    Vfy is the final velocity in the y-direction
    Viy is the starting or initial velocity in the y-direction
    ay is the y-component of the acceleration vector
    xy is the total distance moved in the y-direction

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