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a.
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A
particle is moving at a constant speed v in a circular path of radius r.
Derive expressions for
i) the
angular displacement in a given time interval, Dt, |
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Suppose the particle moves from P to Q in Dt. |
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The distance travelled is
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The angular displacement is
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ii)
the angular speed, |
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The angular speed is
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iii)
the centripetal acceleration. |
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Suppose the particle moves from A to B in Dt. |
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The velocity vector changes from 
to  . |
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The change in velocity is
as shown in Fig.iii. |
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For small angle Dq,
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Thus, the acceleration is
or
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From Fig iii, the direction of this acceleration
points towards the center. |
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| b. |
Describe
an experiment to verify the expression for the centripetal acceleration,
stating the necessary equations for any motions involved. |
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Attach a pendulum bob to some iron washers
through a string that passes through a hollow plastic tube. |
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Put a paper marker on the string somewhere
above the iron washers. |
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Swing the plastic tube. Increasing the speed
of the swing until the paper marker is just below the tube. |
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Count the number of turns n. Then measure
the mass of the iron washer W and the length l. |
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Repeat the experiment for different values
of l and W. |
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If the theory is correct, the horizontal component
of the tension in the string provides the centripetal force:
where W being the weight of the iron washers is also the tension
in the string,
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Thus, we have
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By comparing the quantity 
with W, the equation for centripetal acceleration can be verified. |
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