Physics in Animation: The Law of Inertia

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Get ready to be swept off your feet because today we’re talking inertia! Yep, that’s the physical principle that might literally sweep you off your feet during a bus ride and tosses you around in a roller coaster seat. Now, prepare to find out why it is important for your animation! Professor Alejandro Garcia, who teaches the course “Physics of Animation” at San José State, has returned to tell us about this law of nature that constantly influences you, me, or even a bowl of noodle soup whether still or in motion.

In Part 1 of this series I explained how knowing a little physics will help you observe motion in the real world and, if you want to, create animated motion that’s believable. The principles you’ll learn apply to everything from a simple ball bounce to doing a complicated shot, such as a fight scene.

As mentioned in Part 1, here is my list of the “Principles of Animation Physics”:

The first principle, Timing, Spacing, and Scale, was covered in Part 1; in this posting you’ll learn the Law of Inertia, also known as Newton’s First Law of Motion.

Principle #2: Law of Inertia

The Law of Inertia says that a character will move with constant velocity unless acted on by an unbalanced force. First, let’s be clear what’s meant by an “unbalanced force.” The simplest form of the Law of Inertia is when there are no forces at all (e.g., an asteroid flying in deep space). In that case the  object moves with constant velocity (i.e., constant timing and spacing with a path of action that’s a straight line).

Here’s a more down-to-earth example: A rock sitting on a table has two forces on it: gravity pulling downward and the table’s surface pushing upward; these two forces balance each other. A bowling ball rolling on a smooth floor has a similar pair of balanced forces (gravity and the floor) and, again, these two forces balance.  Since the forces are balanced the bowling ball rolls with constant velocity. If there’s friction on the bowling ball then that’s an unbalanced force and so the velocity won’t be constant (the ball will slow down).

At first this all seems purely academic until you realize that follow-through in animated motion is entirely due to the Law of Inertia. Let’s take a simple example of a character standing on a moving bus. When the bus suddenly stops the character goes flying forward. Before the bus hit the brakes he was moving with constant velocity and, by the Law of Inertia, he’ll continue moving until an unbalanced force acts to stop him (such as when his face hits the floor).

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A corollary of the Law of Inertia is that a character at rest will remain at rest until acted on by an unbalanced force. This means that what we call “drag” in animation is also entirely due to the Law of Inertia. Suppose our character stands up again after the bus comes to a stop. Now if the bus suddenly accelerates forward then our standing character seems to fall backwards.

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To the passengers on the bus it seems as if there’s a force pulling everything backwards but that’s because they’re moving along with the bus. A stationary observer standing outside the bus would realize that the poor chap that’s falling is actually not moving, he has the bus moving out from under him (see illustration below). The character’s motion is actually the same but it looks different depending on whether the camera is inside or outside of the bus. This reminds us that you have to be careful to consider the effect of the camera’s motion, especially when the camera is accelerating.

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The Law of Inertia also explains the so-called “centrifugal force.” If the bus makes a sudden left turn then the character standing on the bus will continue moving in his original direction, causing him to fall towards the right side of the bus. You experience the same apparent force when you’re in a car that takes a left sharp turn. It feels like you’re pulled towards the outside of the turn (the right side of the car) but in reality your body is simply obeying the Law of Inertia, which causes you to move in a straight line unless acted on by an unbalanced force (such as your seatbelt).

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The Law of Inertia is also very important to keep in mind when animating overlapping action. As characters turn their bodies their hair and clothing drag behind due to the Law of Inertia (an object at rest will remain at rest until acted on by an unbalanced force). Once the hair and clothing are moving they’ll continue moving (i.e., follow-through) by the Law of Inertia. And when a character with long hair turns her head, by the Law of Inertia her hair flies outward, as if pulled away from the head by a centrifugal force.

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Finally, I should mention that when animators talk about creating “weight” what they’re arctually referring to is creating “inertia.” To understand this you have to learn the next Principle of Animation Physics: Momentum and Force. But for that you’ll have to wait for Part 3 of this series. Look for it and all the other Principles of Animation Physics appearing here on Animator Island. See you then!

 

[author] [author_image timthumb=’on’]https://www.animatorisland.com/wp-content/uploads/2011/10/AlejandroGarcia.png[/author_image] [author_info]Professor Alejandro Garcia has taught Physics of Animation at San Jose State since 2009. In 2011 he spent a one-year professional leave as physicist-in-residence at Dreamworks Animation SKG.

Find out more about Animation Physics on his website Animationphysics.org or his YouTube Channel[/author_info] [/author]

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Martin H.
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Martin H.

This is amazing information just like last time! I have been waiting for Part 2 since you posted the other one last year. It was a long wait. Worth the wait.

Also there are a lot of bolded sentences haha. You should pick maybe only a few instead of making so many bolded. It was distracting but I copied it into Word and made it all non-bold and that was easier on the old peepers. 😉

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--MassM--
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--MassM--

At a presentation I recently went to, Kip Thorne, Christopher Nolan, and Dr Brian Cox were discussing the physics of the film Interstellar and they said they ran water simulations and got waves that looked like it does. Computers!

bt78
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bt78

Good post.

Reta B.
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Reta B.

After looking at a handful of articles on physics in general,
I really appreciate your way of teaching. It is about the how
it is applied to animation and that is the best! Thanks,

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Can’t wait for the next one!

Cristian
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Cristian

Great post !! this is really helping me to understand some aspects of animation, that I was really confused about.

Thank you 🙂