Difference between curvilinear and rotational motion

[Like Tony Stark]

Homework Statement

The picture shows a plate of mass $750 kg$, whose centre of mass is in $O$. Determine the tension in $A$ and $B$ after $C$ is cut.

Relevant Equations

$\Sigma \tau =I \alpha$
$\Sigma F=ma$

The solution states that there's no rotational motion when $C$ is cut (the motion is curvilinear), so we can take torques with respect to the centre of mass of the plate. But, isn't it rotating? I think of it as a pendulum, which describes a circular motion. What's the difference? Wouldn't the plate oscillate like a pendulum, describing the arc of a circle?

 

[BvU]

What's the difference?

It doesn't rotate: the angle of e.g. AB wrt the horizontal does not change

 

[kuruman]

It doesn't rotate: the angle of e.g. AB wrt the horizontal does not change

I would clarify this and say that because AB wrt the horizontal doesn't change, the block does not rotate about its CM. Nevertheless the block's CM rotates wrt some point in the sense that the angle between the strings and the vertical changes wrt time. By contrast, a pendulum suspended by a single string rotates both about its CM and the point of support. Just like the Moon shows the same face to the Earth by making one revolution about the Earth in the same time it makes one revolution about its axis, the one-string pendulum shows the same face to the point of support.

 

[jbriggs444]

Back in elementary school we were taught to use the term "rotation" for the circular motion of a rigid object such as a satellite about its own center of mass and "revolution" for the [near-] circular motion of a satellite about its primary.

 

[kuruman]

Back in elementary school we were taught to use the term "rotation" for the circular motion of a rigid object such as a satellite about its own center of mass and "revolution" for the [near-] circular motion of a satellite about its primary.

It's a good distinction whereas "orbital" and "spin" (angular momentum) are more physicky.

 

[Like Tony Stark]

Nevertheless the block's CM rotates wrt some point in the sense that the angle between the strings and the vertical changes wrt time.

That's my doubt. Doesn't the centre of mass of the plate oscillate like the ball of the pendulum?

 

[BvU]

No. It stays 'upright'.

 

[jbriggs444]

That's my doubt. Doesn't the centre of mass of the plate oscillate like the ball of the pendulum?

The center of mass moves back and forth in an arc. Yes.

The plate does not change it orientation during this movement. It stays upright at all times.

 

[Like Tony Stark]

The center of mass moves back and forth in an arc. Yes.

The plate does not change it orientation during this movement. It stays upright at all times.

I got it. Thanks.
And what if I want to calculate the period of its centre of mass? Should I treat all the system as a simple pendulum?

 

[kuruman]

Why not draw a FBD, derive the equation of motion and see if it is the same as that of a simple pendulum?