5 thoughts on “4.11”

  1. When I solved this problem I got the same angular velocity as the one in your solution but when I was solving for Vp I used the equation Vp=Vb+w x rbp which is a little different from your equation so my answer was a little different from yours but I just wanted to know if I have to use Vp because it is on the same wheel as P or is it ok to use Vb?

    1. When solving these types of problems there are many, many choices to make. Thankfully, whichever path you choose should result in an identical solution to any other route you might choose so long as your application of the rigid-body equations is correct.

      Using \vec{V}_p = \vec{V}_b + \vec{\omega} \times \vec{r}_{bp} should give the same result as the equation I used. How different was your answer?

      Have you tried working through it with my equation?

    1. I made an assumption at the start of the problem (namely that \vec\omega = \dot\theta \hat k). I made this assumption partially because it was wrong—to illustrate that we don't need to think too hard about the direction that a body will turn, we just need to know that it will turn. Later in the problem (under the banner "Angular Velocity", in blue) I found that \dot\theta is actually a negative quantity indicating that the angular velocity is in the negative \hat k direction.

      Rather than wasting time trying to figure out what direction a body will turn in advance, just make an assumption and let the math tell you whether it is right or wrong. This isn't to say that you should trust the math blindly—we always must be critical of our work—it is to say that we needn't work ourselves into a frenzy trying to know something before we know it.

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