2 Cords affixed at different points are wrapped on a disc

[Father_Ing]

Homework Statement

See attachment

Relevant Equations

-

The hint says the following:
"Since the cords are inextensible, every particle of a cord must be in circular motion about the point where it is affixed to the ceiling. Therefore, the velocities of the points where the cords are leaving the disc are perpendicular to the string"

Due to the fact that the disc is both rotating and falling downward, isn't the cord also have translational motion? Moreover, the length of each cords always changes; there is no way the cords only undergo rotational motion.

 

[BvU]

isn't the cord also have translational motion?

Yes. Neither the problem statement nor the hint excludes translational motion. But the points where they are affixed to the ceiling are fixed.

Moreover, the length of each cords always changes; there is no way the cords only undergo rotational motion.

I think that is right: the center of mass of each cord moves (both along the cord and perpendicular to the orientation of the cord). But the exercise asks for an instantaneous velocity of the disk center.

$\$

 

[haruspex]

Homework Statement:: See attachment
Relevant Equations:: -

there is no way the cords only undergo rotational moti

As soon as a portion of string has unwound, its distance from the support point is fixed, so it only has that rotational motion. The portion not yet unwound clearly has other motion.