Law of acceleration, part one. So Newton established

three basic laws to explain of the connection between motion and forces. And in some of

the other tutorials, we looked at the law of inertia, and the law of inertia explains

motion when we either have no forces, or only balanced forces. But the more interesting

situation is when we have unbalanced forces that are affecting the motion, and in fact

with unbalanced forces, the motion has an acceleration, and that’s what we will look

at now. This law of acceleration is also called Newton’s second law of motion. So just to

remind you, when there is no force or if there are balanced forces, then an object moves

with constant uniform motion. So the simplest example: something floating in space absolutely

no forces on it, just moves with a constant speed, constant direction in a straight line.

But if we have balanced forces, like this bowling ball rolling on the floor, we have

the force of gravity that would be pulling down the ball, but this force of gravity is

balanced by the support force of the floor, and those two are in balance and if we have

negligible of friction, then these two balanced forces lead to, again, constant uniform motion,

constant speed, motion in a straight line. Now the law of acceleration the first part

of law of acceleration says that: objects always change their velocity in the direction

of the unbalanced force. So if we take this asteroid that’s moving through space, and

there is no force on it, if instead we had a force acting in the downward direction,

then the asteroid would change its motion, and its velocity would change in the direction

of that force. So notice that the asteroid is not moving straight downward, but its motion

is deflected in that direction. The horizontal spacings actually stay uniform and the vertical

spacings slow out in the direction of the force. We saw some of this already when we

looked at parabolic arcs. Here’s another situation, let’s say that we have a force that, in the

first case, an object is moving from left to right, and the force is acting from left

to right, well what’s going to happen is the object is going to slow out or accelerate

in that direction. Similar situation occurs if the object is instead moving right to left,

while the force is still left to right. In this case, the object is going against the

force and this results in a deceleration. In physics, we actually refer to this, also

being an acceleration, just in the negative sense, but the more familiar way of expressing

this is that it’s decelerating or in terms of animation, that slows in. Now you’ve already

met the sort of situations because in the first case, this is like a ball that’s falling

downward and slows out as a falls and in the second case, it is like a ball that is rising

and is slowing into the apex. Again, in both cases, the object is changing its velocity

in the direction of the applied force. Now it gets more complicated if the direction

of the motion is all perpendicular or at an arbitrary angle from between the direction

of the motion and the force. So in this more general case, we have a deflection of the

path of action, the spacings are affected so, in this case, the ball is being acted

on by force, which is up and to the left, and so it slows in, moving from left to right,

and it is slowing out in its motion from bottom to top. This really is fairly intuitive if

you think about a force pulling on an object, and in that direction when objects are already

moving in this other direction. Now let’s consider some more cases of a force pulling

on something and the direction, and how that affects the motion. So what we’re going

to look at here is a spool, like you see in this picture that has a string, and in the

first case we have the string wrapped so that it’s looped over the top, and we’re going

to pull on the string and then we’re going to repeat that, but in the situation where

the school is flipped, and we have the string looped all underneath. So let’s just see what

that looks like. So you were probably surprised that in the second case, the spool again moves

from right to left, but this is just reinforcing what was said about the law of acceleration

that objects always change their velocity in the direction of the applied force. So

the applied force is right to left and so the spool slows out in that direction. Let’s

do a very similar example, where we pull on the pedal of a tricycle with the string and

in what direction is the tricycle going to move? Let’s look at that video. So here’s

the tricycle, there’s a string attached to the pedal. Now watch very carefully the position

of the pedal on the screen as we pull. So you see that once again, the motion is in

the direction of the applied force, and in fact, even though you think of the pedal as

rotating backwards in that orientation as the wheels turning, in reality, the pedal

is always moving from right to left in the same direction as the applied force. Now let’s

look at something else about the law of acceleration, that when we have two or more forces in order

to determine the acceleration, we need to determine the net force, which is also called

the total force. So if we have a situation where a 10 pound is falling, but there’s a

significant amount of air resistance acting on the cat, so in this case the force of gravity

would be 10 pounds, the force exerted by a resistance supposedly 7 pounds, that means

that the net force on the cat would only be 3 pounds, and so the acceleration would be

determined by that net force. And in fact, the law of acceleration tells us that the

motion only depends on the net force, not on the individual forces, so we don’t have

to worry about the individual forces, say these guys pushing on this boat, all we have

to do is find the net force by adding up all of their the combined forces to determine

the motion. Now adding up these forces can be a little complicated if the forces are

pulling and pushing all different angles, but aside from that computational detail,

the law of acceleration tells us that: once you find the net force, that’s going to tell

you the acceleration. And in fact, the situation that we’ve been discussing about having balanced

forces, that’s the same thing as saying situation when we have balanced forces, that’s when

net force is zero. So in the simple situation, the sack sitting on the floor, force of gravity

pulls down, the floor pushes up with the same amount of force, but in the opposite direction.

These two forces when we add them up, they add up to zero, and so the net force is zero,

and that’s going to tell us from law of acceleration that the acceleration is zero. Basically what

we already know from the law of inertia. So in summary, the law of acceleration explains

the link between forces and motion, this is Newton’s second law of motion, mathematically

with the expression is f=ma. The first part of the law of acceleration says that objects

always change their velocity in the direction of the unbalanced force. When we have multiple

forces, then we need to add them up in order to find the net force or the total force,

and that is what’s going to tell us the acceleration, and again this acceleration only depends on

the net force, we don’t have to worry about the individual forces. So this is the first

part of the law of acceleration, in the next tutorial, part two, we will specifically connect

how much acceleration we have, what is the timing and spacing look like depending on

the force, in particular depending on how the force on an object compares with the weight

of an object. So that will be in part two. So we’ll see you then.

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