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Instantaneous Axis of Rotation

A disc of rad...

Question

A disc of radius $0.2 m$ is rolling with slipping on a flat horizontal surface, as shown in figure. The instantaneous centre of rotation is: (the lowest contact point is O and centre of disc is C)

A

zero

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B

0.1 m

above O on line OC

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C

0.2 m

below O on line OC

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D

0.2 m

above O on line OC

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Solution

The correct option is C $0.2 m$ below O on line OC
If instantaneous centre of rotation is P at a distance r from the centric line OC, then from the definition of instantaneous centre of rotation, the velocity of point P should be zero.
$v_{p} = 4 - 10 r = 0$
$r = \frac{2}{5} m = 0.4 m$
So, instantaneous centre of rotation is at distance 0.2 m from O (below O) on line OC.

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