## Related questions with answers

The disk rolls without sliding on the fixed horizontal surface. At the instant shown, the instantaneous center of zero velocity for rod $A B$ would be located in which region? $(a)$ Region 1 $(b)$ Region 2 $(c)$ Region 3 $(d)$ Region 4 $(e)$ Region 5 $(f)$ Region 6

Solution

VerifiedThe instantaneous centre of rotation for rod $AB$ can be found at an intersect of lines perpendicular to velocities of points $A$ and $B$.

Point $A$ can only move along the horizontal direction. The disk rolls without sliding, so point $C$ has velocity zero. The velocity of point $B$ is then perpendicular to the line connecting $B$ and $C$.

Instantaneous centre of rotation can then be located at $\boxed{\:\mathbf{a.} \:\text{Region 1}}$, as can be seen on the figure. Here, the situation shown is for clockwise angular velocity of rod $AB$, but the same conclusion can be drawn for counterclockwise direction.

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