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The basic laws of motion were discovered/synthesized by Isaac Newton in the 17^th century. We now know that these laws are not quite right; they are corrected by both relativity and quantum mechanics (as we will see later). For most motion of large objects at normal speed, the corrections are very small and Newton's laws work beautifully well.

Since this is a class on modern physics, we will not spend much time on Newton's laws. However, we still need to discuss them to build a foundation for what is to come.

What is a force

This is very important. A force is an interaction between 2 objects. There are always at least 2 objects interacting - your job in physics is generally to figure out what the 2+ interacting objects are. Second thing: a force manifests itself as a push or pull . That is how we get to First Law below:

The First law.

Every object in a state of uniform motion will remain in that state of motion unless an external force is applied to it.

This is the most misunderstood of the three laws. It says that if there is no force acting on a object, the object will remain in motion at constant velocity and travel in a straight line.

This law essentially defined the notion of an inertial reference frame as we discussed in the week about space-time. At observer moving at constant velocity is an observer for which the laws of Nature look the same as if the velocity was zero (observer at rest).

The Second Law.

An unbalanced force causes an object to accelerate. This is often mathematically expressed by

F= ma . The force which is causing an object to change its movement equals the mass of the object times its acceleration.

Acceleration measures the change in velocity per unit of time. Remember: change is written using the \Delta symbol which means the difference between the end and beginning.

a = \frac{\Delta v}{\Delta t}

Here's the breakdown of that equation:

The time interval between some initial time t_i and some final time t_f is expressed as \Delta t = t_f -t_i .

During this time interval, the velocity of the object may change from initial value v_i to some final value v_f . Again the change in velocity is \Delta v = v_f-v_i . Remember that velocity has a sign, negative if you move left or positive if you move right.

So acceleration can also be positive or negative, because velocity has a direction. For example, when you go east at 20 m/s and change to go west at 20 m/s in a span of 4 seconds, the acceleration would be

a = \frac{20 - (-20)}{4} = 10\ m/s^2

We will not use acceleration very much in this class. Instead we will use change in momentum which is nearly the same thing - and more useful than acceleration for modern physics!