Condition for rolling without slipping (8-13)

Question 1 of 3

Question

$\textbf{Angular speed}$ of the object’s rotation

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Question

$\textbf{Radius}$ of the object

{"title":"Speed of the center of mass of a rolling object","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"6,18,38,52\"}]"} {"title":"Radius of the object","description":"Correct!","type":"correct","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"168,9,198,55\"}]"} {"title":"Angular speed of the object’s rotation","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"210,18,250,56\"}]"}

Question

$\textbf{Speed}$ of the center of mass of a rolling object

{"title":"Speed of the center of mass of a rolling object","description":"Correct!","type":"correct","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"6,18,38,52\"}]"} {"title":"Radius of the object","description":"Wrong","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"168,9,198,55\"}]"} {"title":"Angular speed of the object’s rotation","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"210,18,250,56\"}]"}

Review

Equation 8-13 says that there is a direct proportionality between the linear speed $v_\mathrm{CM}$ and angular speed $\omega$ of a circular object that rolls without slipping. As the wheel in Figure 8-13 rolls downhill it gains speed so $v_\mathrm{CM}$ increases, and it rotates faster so $\omega$ increases, but these increases are always proportional to each \perpher so that $v_\mathrm{CM}$ and $\omega$ are always related by Equation 8-13.