And with velocity, we can derive your position x relative to the stationary frame. Again, x0 is
your initial position
x = (v0 + V)t + x0 (30)
However, since velocity must not be changing under an inertial frame, we can assume V moves
along an axis, which we will take to be the x-axis. If we assume 3D and let x =< x, y, z >, the
above can be written as
8
>
<x = (v0x + V )t + x0
y = v0y t + y0 (31)
>
:
z = v0z t + z0
This allows us to transform the coordinates of an object in a stationary frame to a frame that’s
moving at some velocity.
8 Newton’s Laws
Now that we understand how things move, we must move on to understand why things move.
Newton theorised that objects move because of the influence of forces. A force has units of
Newtons, and can be thought of as a push or pull. Newton’s three laws revolve around forces.
They are
1. An object will continue its original path in a straight line, under constant velocity if not
acted upon by a force
2. The total force acting on an object is proportional to its acceleration and they are related
by the mass of the object
3. Any two interacting objects will experience a force equal in magnitude but opposite in
direction
These three laws explain almost all phenomena we experience in our day to day life. To define
a force mathematically, we must invoke newton’s second law.
X
F ⌘ ma (32)
P
Where F is the total force and m is mass. To find the total force, we simply add up all the
individual forces acting on the object. Mass is how much matter is in the object. If we have
two objects, A and B where A exerts a force on B, we can write newton’s third law as
FA on B = FB on A (33)
These are called ”third law pairs”. Note that these pairs are always found on two di↵erent ob-
jects - the ”source” and the ”object”. There can never be a third law pair acting simultaneously
on a single object. An example of a third law pair is you and the earth. The earth exerts a
force of gravity on you and so, you exert the same magnitude of gravitational force on the earth.
From this logic, it seems that when you jump, not only would you accelerate towards the earth,
the earth would also accelerate towards you! But since the earth is so massive, its acceleration
towards you as a result of your gravitational force would be small. Another example is in strings
- if a string is taut, the magnitude of tension on one end will equal that of the other end.
11
your initial position
x = (v0 + V)t + x0 (30)
However, since velocity must not be changing under an inertial frame, we can assume V moves
along an axis, which we will take to be the x-axis. If we assume 3D and let x =< x, y, z >, the
above can be written as
8
>
<x = (v0x + V )t + x0
y = v0y t + y0 (31)
>
:
z = v0z t + z0
This allows us to transform the coordinates of an object in a stationary frame to a frame that’s
moving at some velocity.
8 Newton’s Laws
Now that we understand how things move, we must move on to understand why things move.
Newton theorised that objects move because of the influence of forces. A force has units of
Newtons, and can be thought of as a push or pull. Newton’s three laws revolve around forces.
They are
1. An object will continue its original path in a straight line, under constant velocity if not
acted upon by a force
2. The total force acting on an object is proportional to its acceleration and they are related
by the mass of the object
3. Any two interacting objects will experience a force equal in magnitude but opposite in
direction
These three laws explain almost all phenomena we experience in our day to day life. To define
a force mathematically, we must invoke newton’s second law.
X
F ⌘ ma (32)
P
Where F is the total force and m is mass. To find the total force, we simply add up all the
individual forces acting on the object. Mass is how much matter is in the object. If we have
two objects, A and B where A exerts a force on B, we can write newton’s third law as
FA on B = FB on A (33)
These are called ”third law pairs”. Note that these pairs are always found on two di↵erent ob-
jects - the ”source” and the ”object”. There can never be a third law pair acting simultaneously
on a single object. An example of a third law pair is you and the earth. The earth exerts a
force of gravity on you and so, you exert the same magnitude of gravitational force on the earth.
From this logic, it seems that when you jump, not only would you accelerate towards the earth,
the earth would also accelerate towards you! But since the earth is so massive, its acceleration
towards you as a result of your gravitational force would be small. Another example is in strings
- if a string is taut, the magnitude of tension on one end will equal that of the other end.
11
