Tilt the thread upward.

A cotton reel has an inner axle of radius r and outer rims of radius R = 2r. Its thread comes off the axle and is pulled at an angle θ above the horizontal. For which θ does the reel roll neither forward nor backward?

A cotton reel on the floor whose thread leaves the inner axle and is pulled at an angle θ above the horizontal; the axle radius is half the rim radius.

Answer: 60°.

The reel does not turn about the contact point when the line of the pull passes straight through that point, because then the pull has no torque about it. The thread leaves the axle along a tangent, at a distance r from the centre.

\cos θ = \frac{r}{R} = \frac{1}{2}

\Rightarrow θ = 60 °

At angles below 60° the reel rolls towards the pull; above 60° it rolls away and the thread unwinds. At exactly 60° it can only slide, which is the classic trick of the obedient reel.

Original practice question · JEE Physics Decoded

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