Motion of an open garage door as it closes

[Andrew1234]

Homework Statement

Explain the relationship between the angular and linear velocities of the panel when the door is fully open, that is, when point E strikes the floor.

Relevant Equations

Work energy principle

If an analogy is drawn to kinematics problems in which for example a ball is thrown from a height h, when it strikes the floor it has a final velocity although it stops moving instantaneously. But in this problem, the points B and D have no linear velocity when E strikes the floor. Their final angular velocities, on the other hand, are equal and nonzero. I don't understand the reason for this discrepancy. At the instant both panels stop moving linearly they should also have no angular velocity. Also, using the analogy of the ball, if an object thrown from a height h has a final linear velocity although it too stops moving in an instant I don't see how the motion of the panels differs in this respect, since they too have a final linear and angular velocity, both of which should instantaneously become zero.

 

[haruspex]

Explain the relationship between the angular and linear velocities of the panel when the door is fully open, that is, when point E strikes the floor.

As the door reaches fully open, point E will strike point A.
Do you mean, fully closed?

the points B and D have no linear velocity when E strikes the floor. Their final angular velocities, on the other hand, are equal and nonzero. I don't understand the reason for this discrepancy.

Why is that a discrepancy? Each panel will be rotating about its own centre.

if an object thrown from a height h has a final linear velocity although it too stops moving in an instant I don't see how the motion of the panels differs in this respect, since they too have a final linear and angular velocity, both of which should instantaneously become zero.

As with a ball hitting the floor, it might strike a barrier. Why is that a problem?

 

[Andrew1234]

According to the solution to the related example problem in the book B and D have no linear velocity because they are at the lower limit of their respective motion ranges. I don't see why the angular velocities are not also zero, because the panels must also stop rotating.
Also from this reasoning if a ball strikes the floor it too is at the lower limit of its motion range but its velocity is not zero but
sqrt (2gh) which is not consistent with how this reasoning is applied to the panels.

 

[lewando]

The door comes to a stop due to a "stopping mechanism". If you were to remove this constraint, the door would oscillate between this shape "<" and this shape ">". The floor provides a similar "stopping mechanism" for your ball analogy.

 

[haruspex]

from this reasoning if a ball strikes the floor it too is at the lower limit of its motion range but its velocity is not zero but
sqrt (2gh) which is not consistent with how this reasoning is applied to the panels.

As I wrote in post #2, and has been echoed in post #4, the rotation stops because it strikes a barrier. This is exactly the same as a falling object hitting the ground.