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Correlation to Linear Motion

A plank is mo...

Question

A plank is moving with a velocity of $4 m / s e c$ . A disc of radius $1 m$ rolls without slipping on it with an angular velocity of $3 r a d / s e c$ as shown in figure. Find out the velocity of centre of the disc.

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Solution

Since it is pure rolling the velocity of the point at the bottom will be equal to velocity of plank.
So at $A$
$V_{c m} - R W = 4 V_{c m} - 3 = 4 \Rightarrow V_{c m} = 7 m / s$

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