# Newton's second law of motion

Which three quantities are connected by Newton's second law?

## Newton's second law of motion

Newton's First Law tells us that a force is needed, in order to change speed or direction. But how much force is needed? This is something Newton's Second Law of motion helps us figure out. Let's compare two situations. Michael and Philip push a skateboard each.

It takes more effort to get something moving if it has more mass, compared to something with less mass. Also, it takes more effort to slow down something with more mass, than something with less mass. Whether you increase or decrease speed, you change the velocity of an object. And, in physics, we call all changes in velocity: acceleration. So, to slow something down, is also to accelerate.

We start to see a pattern here: The larger the mass an object has, the more force is required to accelerate it. Philip's skateboard has twice the load compared to Michael's. If Philip wants to accelerate his skateboard as much as Michael's, he has to push with twice the force. And this is true whether he wants to increase speed… ... or decrease it.

Three things are connected: Acceleration, Force, And mass. More force gives more acceleration. And the larger the mass, the more force is required to accelerate. We can state it like this: Acceleration equals force divided by mass. Look at the fraction on the right hand side.

There are two ways to increase the acceleration: Either, you can increase the force, or, you can reduce the mass. We can re-write it like this too, to get force alone on the left hand side. Force equals mass times acceleration. F equals M times A... This, is Newton's Second Law of Motion.

Newton's Second Law of Motion tells us, that if we push something twice as hard, it'll accelerate twice as much. Look here: The force F affects the mass M. The mass M changes its velocity with acceleration A. Then we double the force to two F. Now the mass is accelerating with two A.

The more force, the more acceleration, as long as the mass is the same. Two F equals M times two A.What about this one then? What about this one then? Let's double the mass too, to two M. Newton's Second Law tells us that we have to push twice as hard to give an object with twice the mass the same acceleration.

Two F equals 2 M times A! Go ahead and pause the video here, and make sure that you understand these two examples. Newton's Second Law adds to the first law. Newton's First Law tells us that a force is required to get a change in speed or direction. Newton's Second Law tells us that as long as a force is acting on an object, it'll keep accelerating.

If we remove friction and air resistance, this is easier to show. We place Philip in space, with a jet pack. As long as his rocket is firing, providing force, the speed is increasing. When Philip turns off the rocket, and stops providing force, he continues with the same speed and in the same direction. But as long as the rocket is firing, and adds force, the acceleration continues.

F equals M times A.