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‫Welcome back.

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‫Before we go into the heart of dynamics, there are a couple of concepts that I want to make sure that,

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‫you know, first of all, let's discuss about dot and cross products.

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‫When dealing with vectors, you can have two types of multiplication, a DOT product and a cross product

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‫when you perform a DOT product.

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‫The answer is always a scalar.

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‫Adult product is very simple.

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‫Say that you have two vectors.

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‫The one vector equals A, B and C, and then the two equals D, E and F.

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‫The dot product of them is computed like this.

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‫The one vector dot, the two vector equals this is the one vector dot.

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‫This is the V two vector and all that equals a times D.

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‫So this times this plus B times E this times this and plus C times F this, times this.

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‫And when you compute that you see that you will just have a scalar here.

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‫Right.

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‫If you look at this form, you won't have a vector, you will have one number and that's why it's a

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‫scalar.

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‫A very simple example where a dot product is used is in computing work, in physics work has the units

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‫of energy, which is Jewelz, and it is defined like this work equals the force vector dot the displacement

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‫vector.

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‫So the work has the units of joules.

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‫So it means that the work measures the energy spent.

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‫Then force has the unit of neutrons and displacement.

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‫The unit of Meaders.

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‫Suppose that you have a ball floating in space and there is no gravity force, no friction, nothing.

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‫And you apply a forward force of five Newtons to it.

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‫Let's call it force applied f a due to that force, the ball travels 10 metres in the X direction.

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‫Since it's a two dimensional problem, you have X here and then you have Y dimension here in this direction.

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‫Since it's a two dimensional problem, your force vector and your displacement vector are two dimensional.

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‫Your force vector is like this, the X component is five Newtons and the Y component is zero Newtons.

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‫And the displacement vector is like this, the X component is ten metres and the Y component is zero

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‫metres.

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‫And here's the meaders.

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‫And now you have to compute how much work this applied force does since in this entire system you only

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‫have one force.

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‫Therefore the work is done only by one force f applied and you compute the work like this w equals the

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‫force applied vector that the displacement vector or like this, the force vector that the displacement

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‫vector equals five times ten plus zero times zero equals.

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‫And I'm going to write it here.

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‫Fifty joules.

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‫So work in physics is a scalar quantity.

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‫Keep in mind that here it does not matter how fast the ball travels the distance.

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‫The concept of work does not care about time.

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‫If you care about time, then you have to divide work by the time spent.

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‫So if it took you two seconds to move the ball forward by ten metres, then work divided by time spent

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‫or W divided by T equals fifty joules divided by two seconds and you will get twenty five joules per

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‫second or in other words, twenty five watts and watts.

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‫Is the unit of power, so the concept of power does take time spent into account.