How Do You Calculate Angular Velocity in a Rolling Wheel Problem?

[medinaj2160]

Homework Statement

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(to see the picture of the problem deleted the spaces in the link provide above. I'm not allowed to post pics because I don't have 15 post

the wheel shown rolls without slipping on the horizontal surface. At the instant shown, the wheel has an angular velocity of 6 rad/s clockwise. Determine the angular velocity of both links at this instant.

Homework Equations

Vb= Va + Vb/a = Va + rb/aw et= Va + wk X rb/a (w is the angular velocity)

The Attempt at a Solution

You are supposed to come up with two equations at common point, then equate them and solve for the unknowns.

I need Wbc, Wba, and Vc at point C

So far I got:

Vb= Vc + Wbc X rb/c

rc/b= -10i + 3j
Vb= Vbi
Wbc= Wbck
and Wbck X -10i + 3j= -3Wbci - 10Wbcj

You can solve this problem by (instantaneous center of zero velocity) doing the problem this way I got Wbc=.57471rad/s, Wba=1.2rad/s, and Vc=6 but I think is wrong because I'm not getting the same answer.

please help

thanks

 

[KataKoniK]

!

Thank you for posting your question. It appears that you have made some progress in solving the problem, but there are a few things that need to be clarified before we can help you further. First, can you provide the full problem statement and any other relevant information? This will help us understand the context of the problem and provide a more accurate solution.

Additionally, it would be helpful if you could explain your approach in more detail. What equations have you used and how did you arrive at them? This will allow us to better understand where you may have gone wrong and guide you towards the correct solution.

In the meantime, here are some general tips for solving problems involving rolling without slipping:

1. Draw a clear and accurate diagram of the system, labeling all relevant points, distances, and angles. This will help you visualize the problem and identify any assumptions or simplifications you may need to make.

2. Write down all known information and equations that relate to the problem. This includes any given values, relevant equations, and any other relevant information.

3. Identify the unknowns in the problem. In this case, it appears that you are trying to find the angular velocities of both links at a given instant.

4. Use kinematic equations to relate the velocities and angular velocities of different points on the system. In this case, you have correctly used the equation Vb = Vc + Wbc X rb/c.

5. Use the principle of conservation of angular momentum to relate the angular velocities of different points on the system. In this case, you can use the equation IaWa + IbWb = IcWc, where I is the moment of inertia and W is the angular velocity.

6. Set up a system of equations using the information and equations you have gathered. This will allow you to solve for the unknowns.

7. Solve the system of equations to find the desired unknowns.

We hope this helps. If you can provide more information and explain your approach in more detail, we will be happy to assist you further. Good luck with your problem!





Scientist at [Your Institution]

 

[piercas]

Hello,

First of all, I would like to commend you for your attempt at solving the problem. It shows that you have a good understanding of the concepts involved in relative velocity.

To solve this problem, we need to use the concept of instantaneous center of rotation (ICR). This is the point where the velocity of all points on the rotating body is zero. In this case, the ICR is at point C.

Using the equations you have mentioned, we can set up the following equations:

Vc = Wbc x rc/b = -3Wbci - 10Wbcj

Vc = Wba x rc/a = 4Wbai - 6Wbaj

Equating these two equations, we get:

-3Wbci - 10Wbcj = 4Wbai - 6Wbaj

We know that the angular velocity of the wheel is 6 rad/s clockwise, so we can write:

Wbci = -6 and Wbaj = -6

Substituting these values in the equation, we get:

-3(-6) - 10Wbcj = 4Wbai - 6(-6)

Solving for Wbcj, we get Wbcj = -0.6 rad/s

To find the angular velocity of the bar AB, we can use the equation:

Wba = Wba/a + Wba/b = -6 + Wbaj = -6 - 6 = -12 rad/s

Therefore, at the instant shown, the angular velocity of the bar AB is -12 rad/s and the angular velocity of the bar BC is -0.6 rad/s. I hope this helps. Keep up the good work!