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I came upon this while wondering whether the friction of a rolling cylinder on an inclined plane depends on the value of friction coefficient.

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now, $$f\leqq\upsilon N$$

Again after calculating I found that the $$f=\frac{mg\sin\theta}{3}$$ So,$$\frac{mg\sin\theta}{3}\leqq \upsilon mg\cos\theta$$ $$\Rightarrow \tan\theta\leqq 3\upsilon$$ But, I can set the angle and mu to be such that this relation does not hold!

What will happen then? Please explain.

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soumyadeep
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1 Answers1

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This problem is an example of rolling without slipping. A very good explanation of this concept is given here. In this case, it implies that rolling without slipping occurs if $\tan \theta \leq 3 \mu$. The expression validates one's intuition too. Its easy to observe that a cylinder tends to roll without slipping when kept on a wedge with lesser slope.

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Sandeep Thilakan
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