Rotating on a small platform attached by massless rods to a pivot

[Doc Al]

Thanks, what about the second part of the question:

How long does it take for Bob to get his snack?

You've presumably found $\omega$, now use it. How many radians must he traverse to reach the banana?

 

[FlipStyle1308]

Radians = pi, right?

 

[Hootenanny]

Radians = pi, right?

What do you mean by that?

~H

 

[FlipStyle1308]

He travels a total distance of pi, which is the distance of 1/2 a circle.

 

[Hootenanny]

He travels a total distance of pi, which is the distance of 1/2 a circle.

Yeah, that's right (sorry I didn't read the Doc's post above). Yes, he must travel pi radians to reach his prize.

~H

 

[FlipStyle1308]

What other info do I need? Is it w initial and w final? Is the w I found the initial or final?

 

[Hootenanny]

What other info do I need? Is it w initial and w final? Is the w I found the initial or final?

The monkey's $\omega$ is given to you (70 rad\s). You should have found the $\omega$ of the monkey and the platform rotating about the central pole, (this should be negative).

~H

 

[FlipStyle1308]

So pi = [(70 + 0.707)/2]t ? By the way, on WebAssign, when I put in my answer of -0.707 for the first part of the question, it was wrong, but when I put 0.707 without the -, it was correct, so I guess I have to use 0.707 in this equation. But is this the right equation to use?

 

[Hootenanny]

So pi = [(70 + 0.707)/2]t But is this the right equation to use?

No. The 70 rad/s is simply how fast the platform is rotating about its own axis, not how fast the platform is rotating about the central pole. You need to use the 0.707 rad/s, this is a constant speed (because no net torques act). You can simply use speed = distance/time . Regarding the negative answer, the negative sign simply indicates that the platform is rotating about its own axis in the opposite direction to which it is rotating about the central pole. Do you understand this? I don't think I explained it very well?

~H

 

[FlipStyle1308]

Um...so pi = [(0.707 + pi/t)/2]t ?

 

[Hootenanny]

Um...so pi = [(0.707 + pi/t)/2]t ?

Not quite, its probably so simple your trying to overcomplicate things. As I said above;

$$v = \frac{ds}{dt} \Rightarrow \omega = \frac{d\theta}{dt}$$

$$dt = \frac{\theta}{\omega}$$

Where $\omega$ is the angle of travel in radians.

Can you go from here?

~H

 

[FlipStyle1308]

So w=d/t, t=d/w=pi/0.707?

 

[Hootenanny]

So w=d/t, t=d/w=pi/0.707?

That's what I'd do

~H

 

[FlipStyle1308]

Thank you!