This Spool may Fool you!

Classical Mechanics Level 2

A spool is a cylindrical device, which has discs fixed at its ends that have bigger radius than the cylinder.

A thread is wound on the cylindrical portion and its one end is pulled, as shown in the diagram above. If the ground is perfectly smooth (coefficient of friction = 0), how will the spool move?

The spool will move towards the left and rotate clockwise The spool will move towards the left and rotate counterclockwise The spool will move towards the right and rotate counterclockwise The spool will move towards the right and rotate clockwise

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Rohit Gupta by Rohit Gupta , 34, India

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3 solutions

Sravanth C.
Dec 24, 2016

If we look at the free body diagram of the spool carefully, we can observe that the force F F is acting towards the right. Since there is no friction or any form of forces acting in the horizontal direction, the spool will move towards the right.

If we look at the rotational aspect of the spool, the force F F is providing an anti-clockwise torque with respect to the center of mass of the body, hence the spool rotates in an anti-clockwise sense.

22 Helpful 0 Interesting 0 Brilliant 0 Confused

For the force F to provide any torque, the spool has to be PIVOTED ( AT THE CENTRE OF MASS ! ) which is NOT according to the question. If it is pivoted, then there won't be ANY horizontal (or vertical ) motion, but only rotational.

J Wickrama - 4 years, 4 months ago

Ever drop a roll of toilet tissue and try to retrieve it by pulling on the tissue?

Gena Lee - 4 years, 4 months ago

pls explain clearly, because the force exactly tangential to the spool , how it moves the oject toward right

Imran Kabir - 4 years, 4 months ago
Ayush Dube
Dec 30, 2016

There is no friction so the spool will obvio move to the right(because it is pulled that side by the string) It will rotate anti-clockwise because the force is providing an anti-clockwise torque with respect to the center of mass of the body, hence the spool rotates in an anti-clockwise sense.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

For the force to provide any torque, the spool has to be PIVOTED ( AT THE CENTRE OF MASS ! ) which is NOT according to the question. If it is pivoted, then there won't be ANY horizontal (or vertical ) motion, but only rotational.

J Wickrama - 4 years, 4 months ago
J Wickrama
Feb 10, 2017

Really speaking, if there is NO FRICTION at all, the spool will move to Right, but WITHOUT ANY ROTATION, since the only forces acting are; Horizontal: pull, (assumed according to figure), VERTICAL: weight of the spool downwards, balanced by the reaction upwards. There is no rotational force to rotate the spool, (neglecting any air resistance of course !)

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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