When calculating the displacement of a rolling body do we just calculate the displacement due to Vcom in a particular time t or additionally need to consider also the displacement that may be produced because of the rolling motion.
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1 Answer
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For pure rolling (i.e., rolling without slipping) the displacement of the center of mass (COM) is due to the rolling motion. They are not independent.
For pure rolling the linear velocity of the center of mass $v_{COM}$ is related to the angular velocity $\omega$, where $R$ is the radius of the rolling body, by
$$v_{com}=R\omega$$
Where $\omega$ is in radians per second.
Thus
$$v_{com}t=R\omega t$$
For example, if $\omega= 2\pi$ radians per second, after 1 second the angular displacement is $2\pi$ radians and the linear displacement of the COM is $2\pi R$, or the circumference of the rolling body.
Hope this helps.
