Newton’s Third Law of Motion
The law states that for every action force, there is an equal and opposite reaction force. A common confusion is to assume that all forces must be canceled by an equal and opposite force. Clearly, this would lead to a situation where there would be no accelerations in the universe. Since there are accelerations, that interpretation must be wrong. The proper action/reaction force pair will always act on different bodies. I push on my chair and my chair pushes back on me.
In defining the system for the application of the Third Law, we should note that an object cannot exert forces on itself to produce accelerations, since this would include internal forces which are not considered in the application of Newton’s Laws. In making a rocket ship travel, gases are exhausted. The rocket pushes on the gases to expel them. The gases must, therefore, push back on the rocket. This is rocket propulsion.
In firing a rifle the force ejecting the bullet and the recoil force of the rifle are the same (action/reaction force pair). But the bullet has small mass and therefore can achieve very high acceleration (a = F/m). By contrast the great mass of the rifle causes a small acceleration of the rifle with this same force. (a = F/M).
This chapter also covers principles of vectors. A vector is a quantity that has size (magnitude) and direction. It is represented by an arrow. The length of the arrow gives the magnitude of the vector and the orientation of the arrow gives the direction of the vector. The components of a vector refer to the projections of the vector onto a set of mutually perpendicular coordinate axes. Imagine a vector drawn from the origin of a Cartesian (x-y) coordinate system. Drop a perpendicular from the tip of the vector to the x-axis. The x-component of the vector is the vector from the origin to this perpendicular. Dropping a perpendicular to the y-axis from the tip of the vector gives the y-component in a similar fashion.
Vector addition is easily done by arranging the vectors “tip-to-tail” this is, at the end of the first vector start the second one and so forth until you have used all of the vectors in the sum. The vector sum is a vector from where this process started to the tip of the final vector. Note that if Ax and Ay are the x- and y-components of vector A, then
shows a simple vector sum and reinforces the idea that the components are themselves vectors.
Vector subtraction is very similar to vector addition. In order to perform , we first form , a vector the same length as but in the opposite direction. We can then apply the rule of vector addition on and .