Game Development Reference
In-Depth Information
'
distance in feet or meters. In a 3D world, we
re going to use the same formulas, but the
inputs are going to be 3D vectors to represent position, speed, and acceleration in 3D
space. Luckily, these vectors work exactly the same as scalar numbers in these equations,
because they are only added together or multiplied by time, a scalar number itself.
Whenever I have a particularly nasty crash when mountain biking, some joker in my
mountain biking group quips,
s
Second Law of Motion and says that force is calculated by multiplying the mass of
the object in question with its acceleration. In the case of an unfortunate mountain
biker taking an unexpected exit from the bike, the acceleration is the change in the
biker
“
F=ma, dood. You okay?
”
This formula is Newton
'
s weight.
Crashing at the same speed, the heavier biker gets hurt more. If the same biker
crashes while riding downhill, the slightly faster speed does quite a bit more damage
because acceleration has a time squared component and is therefore much more seri-
ous than a change in mass.
Force is typically measured in Newtons. One Newton, symbolized by the letter N, is
defined as the force required to accelerate a mass of one kilogram at a rate of one
meter per second squared.
'
s velocity over time, or deceleration actually, multiplied by the biker
'
N
¼ð
kg
Þ
m
=
s
2
Try not to confuse acceleration and force. Gravity is a force, and when it is applied to
an object, it causes acceleration. Galileo discovered an interesting property about this
acceleration by dropping things from the Leaning Tower of Pisa: It doesn
t matter
how much something weighs because they all fall at the same rate, excepting any
large differences in air resistance. This is extremely unintuitive until you remember
that even though more massive objects exert a greater gravitational force, this
force is used to accelerate the larger mass, and therefore the acceleration remains
the same. The only way you get higher acceleration is with stronger gravitational
fields. Feel free to find a black hole and experiment
'
—
I
'
ll watch from a few light years
away.
Who Wins, a Tissue or the Planet?
While it might not feel this way to you, gravitation is an incredibly weak force
compared to something like electricity. You can prove it to yourself by placing
an object, like your cell phone, on a piece of tissue paper. Grab both sides of
the tissue paper and lift it, suspending your cell phone over the ground. The
force that keeps the cell phone from tearing through the tissue paper is
the electrical force binding the material of the tissue paper together. So the
