The question asks: A wheel with a radius of 53.0 cmrolls without slipping along

Question

The question asks:
A wheel with a radius of 53.0 cmrolls without slipping along a horizontal floor. Attime t1, thedot P painted on the rim of the wheel is thepoint of contact between the wheel and the floor, as shown in thfigure below. At a later time t2, thewheel has rolled through one and a halfrevolutions.
So I'm asked to find themagnitude of the displacement of P and theangle (relative to the floor) of the displacement ofP.
I found the magnitude to be197.3822 m and the angle as 32.4816, but my answers are incorrect.I would really appreciate if someone could walk me through this,not just give me the answers. Thanks!


The question asks:

So I'm asked to find themagnitude of the displacement of P and theangle (relative to the floor) of the displacement ofP.
I found the magnitude to be197.3822 m and the angle as 32.4816, but my answers are incorrect.I would really appreciate if someone could walk me through this,not just give me the answers. Thanks!

Explanation / Answer

radius r = 53 cm = 0.53 m No.of revolutions in the given time interval = 1.5 So, linear displacement for one completerevolution S = 2r                                                                                     =3.33 m So, linear displacement for 1.5 revolutions = 1.5S                                                                 = 4.995 m Angular displaement foe 1.5 revolutions = 1.5 *360 degrees                                                                 = 540 degrees                                                                 = 540 * ( /180 )                                                                 = 9.424 rad

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