The figure shows a system consisting of (i) a ring of outer radius 3R rolling clockwise without slipping on a horizontal surface with angular speed ω and (ii) an inner disc of radius 2R rotating anti-clockwise with angular speed ω/2. The ring and disc are separated by frictionless ball bearings. The system is in the x-z plane. The point P on the inner disc is at a distance R from the origin, where OP makes an angle of 30° with the horizontal. Then with respect to the horizontal surface.

Engineering

Physics

Physical Quantities

Question

The point O has a linear velocity $3 Rω \hat{i}$

The point P has a linear velocity $(3 - \frac{\sqrt{3}}{4}) Rω \hat{i} + \frac{1}{4} Rω \hat{k}$

The point P has a linear velocity $\frac{11}{4} Rω \hat{i} + \frac{\sqrt{3}}{4} Rω \hat{k}$

The point P has a linear velocity $\frac{13}{4} Rω \hat{i} - \frac{\sqrt{3}}{4} Rω \hat{k}$

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${\vec{v}}_{0} = 3 ωR (\hat{i})$

${\vec{v}}_{P} = (3 ωR - \frac{ωR}{2} \cos 60 º) \hat{i} + \frac{ωR}{2} \sin 60 º \hat{j}$

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