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Update particle_kinematics.astro
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Minor updates
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mopolz2 committed Sep 7, 2024
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23 changes: 9 additions & 14 deletions src/pages/dyn/particle_kinetics.astro
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Expand Up @@ -382,13 +382,10 @@ import DisplayTable from "../../components/DisplayTable.astro"

</SubSubSection>

<SubSubSection title="Banked turns">
\label sub:PartKin_turns
<BlueText>Complete in "Banked turns". Just the introduction and the information under "Track geometry" and "Point mass model".</BlueText>
<SubSubSection title="Banked turns" id="banked_turns">

<p>
Turning in a circle requires a vehicle to have a <a
href="rvt.html#rvt.sc">centripetal acceleration</a> inwards
Turning in a circle requires a vehicle to have a centripetal acceleration inwards
on the turn, and so there must be some centripetal force
that produces this acceleration. For a vehicle driving on
flat ground, this force must be produced by a sideways
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curve.</li>
<li><a
href="http://www.youtube.com/watch?v=TK59zTPlL4g">Video of
the bus</a> shown in Figure <a
href="#avb‑fc">#avb‑fc</a>.</li>
the bus</a> shown in coach figure.</li>
<li><a
href="http://www.youtube.com/watch?v=MXtfsxhAHfs">Video
taken from inside a car</a> driving around the
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</CalloutContainer>
</SubSubSection>

<SubSubSubSection title="Track geometry">
<SubSubSubSection title="Track geometry" id="track_geometry">
<p>
To understand the dynamics of the bus
above, we first need a simple model of the geometry of
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class="option-toggle:avb-fg-c:vectors" onclick="avb_fg_c.toggleOption('vectors')">vectors</button> for
velocity, acceleration, and force as the bus drives around
the track. We assume constant speed, so there is only an
acceleration <a href="rvc.html#rvc-em">when the velocity
changes direction</a> around the corners. This model assumes
semi-circular track ends, but <a href="avt.html">this is
not a good idea</a> in practice.
acceleration when the velocity
changes direction around the corners. This model assumes
semi-circular track ends, but this is
not a good idea in practice.
</p>
<PrairieDrawCanvas id="avb-fg-c" width="600" height="600">
<p>
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angle \(\theta\) below, then we see that a friction force
\(F\) tangential to the road is needed to keep the bus from
sliding. In practice, this force will be limited by \(F \le
\mu N\), where \(\mu\) is the <a
href="rff.html#rff.sc">coefficient of friction</a>. If we
\mu N\), where \(\mu\) is the coefficient of friction. If we
incline the track until it is nearly vertical, we see that
there a huge friction force would be required but only a
tiny normal force is available. As this would not be
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