2-forces.md

marp	paginate	math	title
true	true	mathjax	Math 2. Forces

2. Forces

What is a force?

• In physics, a force is an influence ("push or pull") that can change the motion of an object

• Force causes an object to accelerate

  • This in turn changes the object's velocity
  • ...which changes the object's position

• Brackeys video: Forces

Force vector

• $\vec{F} = m\vec{a}$
  • the unit of force is Newton ($N = kg \cdot m/s^2$)
  • force equals mass times acceleration
  • the force is a vector
  • so it not only has a magnitude, but also a direction

Note about forces in games

• In games, we're generally more interested in the gained acceleration than the actual force
  • $\vec{a} = \vec{F} / m$
  • The bigger the mass, the smaller the acceleration!

Multiple forces

Force vectors can be added together to acquire the total force:

Torque

• Torque is the rotational equivalent of linear force
• Torque "makes things turn"
• In simplified terms, torque is force times length of the lever arm
• $T_{A} = F_{A} \cdot r_{AO}$
• Unit of torque is Newtonmeter ($Nm = kg \cdot m/s^2 \cdot m$)

Torque... vector?

• More precisely, torque is a vector, produced by a cross product between the lever arm vector and a force vector
  • $\vec{\tau} = \vec{r} \times \vec{F}$
• Note: Cross product between two vectors produces a new vector perpendicular to both the two

Forces in Unity

• In Unity, forces are applied by the physics engine
  • See: Physics
  • We need a Rigidbody component to apply forces to a GameObject.
• If you want more control, you can also create your own code e.g., for simulating planets in a star system

Exercise 1. Forces

Create a 3D scene where a player character can push around rigid bodies by applying a force to them.

How would you calculate the direction of the force?

Hint: you need to use the concepts of distance and normalization.

Reading & Watching

• Physics for idiots: Dynamics