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### Course: Pixar in a Box > Unit 7

Lesson 2: The physics of particle systems- Start here!
- Graphing motion over time
- Position, velocity and acceleration
- Vector addition
- Velocity and acceleration vectors
- Understanding net forces
- Net forces
- Force and acceleration
- Applying gravity to a particle
- Particle collisions
- Particle collisions
- Animating particles
- Particle calculations

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# Vector addition

Every force in our particle system can be represented with a vector, which describes size and direction. Vectors are drawn as arrows, with the tail and head showing direction and the length indicating magnitude. To add two vectors, we use the head-to-tail rule. Place the tail of the second vector at the head of the first vector. Then, draw a new vector from the tail of the first vector to the head of the second vector. This new vector is the sum!

## Want to join the conversation?

- how would you add 3 vectors with the head to tail method?(8 votes)
- In the same way, just put 3rd vector's tail to 2nd vector's head(7 votes)

- Where is the link to the vektors he mentioned?(4 votes)
- Direction and magnitude! Oh yeah!!(4 votes)
- Am I the only one who doesn’t understand?lol(3 votes)
- You should now have a good feeling for the relationship between position, speed and acceleration. Before we can (mumbles) formulas to describe how the particles will move based on the laws of physics, We need to revisit how we think about the speed of the particle. We need to know not only how fast it's moving, but also the direction of motion. In this case downward. We are using idea called a vector to represent things that have both the size and the direction. Vectors are joined as arrows. The direction is which way it's pointing, and the length of the arrow called the magnitude of the vector, indicates it's size. We call this point, the tail of the vector, and this point, the head of the vector. A vector called the velocity, is used to describe the speed and direction of the particle. A short vector means the particle is moving slowly. A long vector indicates that the particle is moving quickly. In this diagram the balls motion is downward, so the velocity vector points downward. If the particle is accelerating, for instance due to gravity, the length of the velocity vector will increase over time since the speed is increasing. Acceleration is also a vector because it too, has a magnitude in direction. But notice the size of the acceleration vector doesn't change as the ball falls. As we saw on the last video, a particle falling under the influence of gravity has a constant acceleration. That is both the direction and size of the acceleration vector is constant. As shown here. We also need to add vectors together. We do this using the head to tail rule. For example, if we need to add vectors v and w, we move w so that v's head is at w's tail. Like this. The resulting vector written v+w, goes from v's tail to w's head. Okay, that's a lot of new ideas. So let's pass here for you to use the next exercise to try this all out. We couldn't make our films without vectors. Vectors are being used any time you see anything moving in our films.(2 votes)
- I'm training to be an youtube animator and this is helping more than ever.(1 vote)
- do you know peter collingridge he isso nice(1 vote)
- Yes, he makes all the simulations.(1 vote)

- this explanation of vectors is really NOT CLEAR !(0 votes)
- Where can we try this all out?

Does anyone have a link?(0 votes) - how would you find the d vector?(0 votes)
- Maybe by seeing where the head or where the tail was at.(0 votes)

## Video transcript

- You should now have a good
feeling for the relationship between position, speed and acceleration. Before we can (mumbles)
formulas to describe how the particles will move
based on the laws of physics, We need to revisit how we think about the speed of the particle. We need to know not only
how fast it's moving, but also the direction of motion. In this case downward. We are using idea called a
vector to represent things that have both the size and the direction. Vectors are joined as arrows. The direction is which way it's pointing, and the length of the
arrow called the magnitude of the vector, indicates it's size. We call this point,
the tail of the vector, and this point, the head of the vector. A vector called the
velocity, is used to describe the speed and direction of the particle. A short vector means the
particle is moving slowly. A long vector indicates that
the particle is moving quickly. In this diagram the
balls motion is downward, so the velocity vector points downward. If the particle is accelerating, for instance due to gravity, the length of the velocity
vector will increase over time since the speed is increasing. Acceleration is also a
vector because it too, has a magnitude in direction. But notice the size of
the acceleration vector doesn't change as the ball falls. As we saw on the last video, a particle falling under
the influence of gravity has a constant acceleration. That is both the direction and size of the acceleration
vector is constant. As shown here. We also need to add vectors together. We do this using the head to tail rule. For example, if we need
to add vectors v and w, we move w so that v's head is at w's tail. Like this. The resulting vector written v+w, goes from v's tail to w's head. Okay, that's a lot of new ideas. So let's pass here for you
to use the next exercise to try this all out. We couldn't make our
films without vectors. Vectors are being used any
time you see anything moving in our films.