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Let's talk about kinetic energy.
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We're calling kinetic
energy K, and it's
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given by 1/2mv squared.
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And this is a scalar quantity.
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So it's going to be
either 0 or positive.
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It's never going to be negative.
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The SI unit for kinetic
energy is joule,
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so we have one joule
here for kinetic energy.
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And the units come from this,
so we have kilogram and then
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meter per second squared.
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Now, let's assume we have an
object that is first at rest
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and then it speeds up with
a certain velocity, which
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means the object is
going to experience
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a change in kinetic energy.
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And so we'll express this
as 1/2mv final squared
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minus 1/2mv initial squared.
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And if we have a
motion, so velocity in,
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let's say a 2D or
a 3D space, then
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we have to consider all
these components here
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and we can also
pull out the 1/2m,
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and then we have
vx final squared
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plus vy final squared
plus vz final squared
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and then minus all the initial
values, x initial, y initial,
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and z initial.
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Now when we consider
just a point particle,
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then we can also ask
what is the momentum?
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How can we pair up momentum
and kinetic energy?
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So I'm writing it again
here, k equals 1/2mv squared.
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If we multiply this by m
upstairs and downstairs,
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we're going to have m
squared over v squared,
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and that's actually p squared.
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Remember p equals mv.
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And so we're going to get that
this actually can be expressed
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as p squared over 2m.
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And so that is
the kinetic energy
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expressed in terms of the
momentum of a particle.