Laws of Motion (Useful Knowledge for Animators)

It was Sir Isaac Newton who in 1687 first set out the universal laws of motion in his groundbreaking treatise the Principal. In it he described three laws that underpin all our subsequent understanding of the physics of motion.

First law (inertia)
Newton’s first law of motion states that every object that possesses weight will remain static until such time that a force is applied to it. So if an object is at rest it will remain that way until an external force affects it. Once an object is moving it will remain moving in a straight line until such time it is acted upon by an external force affecting either its speed or direction.

This explains how the earth and all the other planets in our solar system orbit the sun; if the sun wasn’t there to exert a force (gravity) on these planets, they would simply move out into the depths of space.

Second law (constant acceleration)
The second law states that the motion of an object accelerates in the direction of the force applied to it and that the greater the force applied to an object, the greater the acceleration will be. The greater the mass of an object, the more inertia the object possesses and consequently the greater the force required to move the object.

Simply put – the harder you kick a ball, the further and faster it will travel. Balloons require less energy to move them than tennis balls, which in turn are  easier to move than cannonballs.

Third law (equal and opposite action)
Newton’s third law of motion states that for every action there is an equal and opposite reaction. This means that if a force is applied to a body, the body reacts with an equal and opposite force on the body that exerted the force.

We can see an example of this in rocket travel in space. The hot gases moving out of the back create forward momentum of the rocket. We can also see this in the recoil of a cannon as it fires a cannonball. Notice that the cannon will move much less than the cannonball because of the comparative mass and inertia of the two separate objects.

While friction may not noticeably affect a cannonball rolling along a smooth surface, the action may be slowed a little if it travels over rough uneven ground and may be more quickly stopped if it is rolling across a muddy field, as the friction caused by the mud would be far greater. Try hitting an ordinary party balloon with the flat of your hand and you will observe how quickly it reaches its top speed; you may also notice how quickly it begins to slow down as it moves through the air and meets friction with the air. This peculiar action is due to its size:weight ratio. Its size may be comparable to the cannonball though its mass is much lower. Consequently, it possesses far less inertia and, oncemoving, less momentum.

Cause and effect
So, we have seen that once an object is moving it takes on momentum, which equates to its mass and the speed at which it is traveling. The more momentum an object possesses, the further it will travel and the greater the opposing force needed to bring the object to rest. This principle will be reflected in the animation timing. A light object may get up to its running speed much more quickly than a heavy object that has to overcome far greater inertia. However, the heavier object may continue to move long after the lighter object has come to rest. Motorcycles accelerate and decelerate more quickly than a large lorry, even though the engine size outputs less energy.

Gravity and its effect on a falling object
Newton also described a universal law of gravitation based, it is said, on his observations of apples falling from a tree. However, it was Galileo who observed that all objects, when dropped, fall at the same rate. An American astronaut on the surface of the moon demonstrated this principle, first set out by Newton, most clearly for the entire world to see on television footage. For this purpose he used a hammer and a feather to illustrate the point; they fell at the same rate and landed together. However, this does not take into account air resistance. Back on earth, the feather will obviously fall at a much slower rate than the hammer due to the effect of comparative friction on the objects. When a ball is thrown into the air vertically it will initially accelerate proportionately to the force applied to it; it will gradually slow down until it reaches its apex. The height the ball achieves is determined by the force with which it is thrown. Gravitational forces that apply themselves to the ball counter the initial force applied to the ball. This will result in the ball slowing down until all the energy initially applied to the ball is expended. The ball will then stop, albeit for an instant, before beginning to accelerate as it travels downwards again. If it were possible that the ball could be thrown hard enough it would reach such a height that placed it beyond the gravitational pull of the earth and it would begin to orbit the earth. We can see that the dynamics of a thrown object are not only determined by the force applied to it to make it move in the first place, but also gravitational forces. This gives us a
particularly distinctive arc. A further aspect we need to consider is that objects are a source of stored energy and that the energy can be released in a number of ways. Falling objects release their energy, at least some of it, on impact with the ground in the form of kinetic energy, which is to say they bounce or move off in other directions. We can see clear examples of how the energy within a falling object is expended. The height of a bouncing ball is determined by the height from which it is dropped. The higher the position the ball falls from, the greater the height of the bounce.

It was Galileo who observed that all objects, within a vacuum, undergo uniform acceleration. A large object and a small one, such as a cannonball and a marble, could be dropped from a high building and they would land at the same time. This demonstrates rather beautifully that the effects of gravity are constant and apply equally to all objects, and that all objects accelerate as they fall to earth at a constant speed. The reason the feather lands after the hammer has nothing to do with the effects of gravity, it is friction through air resistance that slows the descent of the feather; a smaller object with the same mass as the feather though with less surface area would accelerate at the same rate as the hammer.

Source: Animation: The Mechanics of Motion

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