‫Welcome back.
‫Before we go into the heart of dynamics, there are a couple of concepts that I want to make sure that,
‫you know, first of all, let's discuss about dot and cross products.
‫When dealing with vectors, you can have two types of multiplication, a DOT product and a cross product
‫when you perform a DOT product.
‫The answer is always a scalar.
‫Adult product is very simple.
‫Say that you have two vectors.
‫The one vector equals A, B and C, and then the two equals D, E and F.
‫The dot product of them is computed like this.
‫The one vector dot, the two vector equals this is the one vector dot.
‫This is the V two vector and all that equals a times D.
‫So this times this plus B times E this times this and plus C times F this, times this.
‫And when you compute that you see that you will just have a scalar here.
‫Right.
‫If you look at this form, you won't have a vector, you will have one number and that's why it's a
‫scalar.
‫A very simple example where a dot product is used is in computing work, in physics work has the units
‫of energy, which is Jewelz, and it is defined like this work equals the force vector dot the displacement
‫vector.
‫So the work has the units of joules.
‫So it means that the work measures the energy spent.
‫Then force has the unit of neutrons and displacement.
‫The unit of Meaders.
‫Suppose that you have a ball floating in space and there is no gravity force, no friction, nothing.
‫And you apply a forward force of five Newtons to it.
‫Let's call it force applied f a due to that force, the ball travels 10 metres in the X direction.
‫Since it's a two dimensional problem, you have X here and then you have Y dimension here in this direction.
‫Since it's a two dimensional problem, your force vector and your displacement vector are two dimensional.
‫Your force vector is like this, the X component is five Newtons and the Y component is zero Newtons.
‫And the displacement vector is like this, the X component is ten metres and the Y component is zero
‫metres.
‫And here's the meaders.
‫And now you have to compute how much work this applied force does since in this entire system you only
‫have one force.
‫Therefore the work is done only by one force f applied and you compute the work like this w equals the
‫force applied vector that the displacement vector or like this, the force vector that the displacement
‫vector equals five times ten plus zero times zero equals.
‫And I'm going to write it here.
‫Fifty joules.
‫So work in physics is a scalar quantity.
‫Keep in mind that here it does not matter how fast the ball travels the distance.
‫The concept of work does not care about time.
‫If you care about time, then you have to divide work by the time spent.
‫So if it took you two seconds to move the ball forward by ten metres, then work divided by time spent
‫or W divided by T equals fifty joules divided by two seconds and you will get twenty five joules per
‫second or in other words, twenty five watts and watts.
‫Is the unit of power, so the concept of power does take time spent into account.