Mistake in Exercises for the Feynman Lectures?

AI Thread Summary
The discussion centers on the interpretation of the velocity components of a point on a rolling wheel, specifically focusing on the angle θ and its impact on velocity calculations. The initial assertion is that the velocity should be expressed as v = V((1+sinθ)i -(cosθ)j), based on the expected behavior of the wheel's motion. Clarification is sought on whether this expression accurately predicts the speed of point P on the rim relative to the ground contact point. The question highlights the relationship between the angle of rotation and the resulting velocity components. Ultimately, a misreading of the question is acknowledged, leading to a better understanding of the problem.
suh112
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Homework Statement
This is problem 14.1 from "Exercises for the Feynman Lectures on Physics":

14.1 A rigid wheel of radius R is rolling without slipping on a horizontal surface. The plane of the wheel is vertical, and the axis of the wheel is moving horizontally with a speed V relative to the surface. If the axis of the wheel is parallel to the z-axis, V is in the positive x-direction, and ##\theta## the angle through which the wheel has rotated since a certain point P on the rim was in contact with the ground, show that the instantaneous velocity (speed and direction) of the point P is given by
v = V ((1- cos##\theta##)i + (sin ##\theta##) j).
Relevant Equations
v = V ((1- cos##\theta##)i + (sin ##\theta##) j)
It seems to me that the answer should be v = V((1+sinθ)i -(cosθ)j) intuitively since ##V_x## should be zero at θ = −π\2 and should be greatest when the angle is 90 degrees. Similarly, the component of velocity in the y direction should be greatest when the angle ##\theta## is 180 degrees and zero when ##\theta## is 0 degrees. Am I doing something wrong?
 

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According to the statement of the question, angle θ is "the angle through which the wheel has rotated since a certain point P on the rim was in contact with the ground". If the wheel rolls without slipping what is the speed of certain point P on the rim relative to the point of contact with the ground? Does the given expression predict that? Does your expression predict that?
 
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kuruman said:
According to the statement of the question, angle θ is "the angle through which the wheel has rotated since a certain point P on the rim was in contact with the ground". If the wheel rolls without slipping what is the speed of certain point P on the rim relative to the point of contact with the ground? Does the given expression predict that? Does your expression predict that?
Oh I misread the question. This makes sense thanks.
 
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Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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