Problem statementSolution video |

**DISCUSSION THREAD**

**Discussion**

As you plan your solution, consider that for the velocity part of the problem, you will need to use a velocity equation for bar AB and two velocity equations for the disk:

- Write the velocity of point B referenced to point A on bar AB.
- Write the velocity of point O referenced to the contact point C on the disk. Note that since the disk does not slip, the velocity of point C is zero.
- Write the velocity of point B referenced to point O on the disk.

These equations together will provide you with the equations that you need for the angular velocities of the bar and disk.

Repeat this same process above for accelerations. Please note that the acceleration of C on the disk is NOT zero - instead, you know that its acceleration is strictly in the y-direction.

Any questions?? Please ask/answer questions regarding this homework problem through the "Leave a Comment" link above.

Are we not allowed to assume the v_b is in one direction? I am a bit confused on how to solve for the velocity equation of B with respect to A.

Oh, I think I see what we are doing here. So we are solving for the velocity of B in terms of v_A, omega, and R. Then we do the same with O. Then in the equation of B/O, we plug in these values to solve for omega?

be careful to differentiate between omega ab and omega disk. They are not the same value.

I was able to find the angular acceleration on the disk, but I am having a hard time finding the acceleration at point C of the disk.

Lorraine: As we have discussed in class, the acceleration of a no-slip point on a disk is r*omega^2 and pointing from the no-slip point to the disk's center.

It is not important to remember the results; you can easily derive it (as detailed in the lecture book). Use the rigid body acceleration equation relating the no-slip point to the center of the disk. The answer comes from the vertical component of that equation.

I'm also having the same problem, and i have already found acceleration of C in y. However I'm not sure how to move on from there since none of my equations require Acceleration of C in y.

Your angular acceleration of AB should be in y in your three acceleration equations

I have that as well, I'm just confused on where I can plug Acy into

Does the bar and the disk have the same or separate angular velocities/accelerations?

Ozan: The bar and disk are separate rigid bodies. As you can see from the animation above, the angular speeds of the bodies are not the same.

Just wanted to make sure I am reading it right, when it says "point B referenced to point A on bar AB" it means in terms of rB/A correct?

Yes because v_A is given, allowing you to put v_B in terms of v_A.

Why do I need to use B in ref to o and C in ref to O. Can I not just do C in ref to B. This seems easier because O has a translational velocity that is unknown and must be solved for while c does not.

The suggestion is more for the acceleration equation than for the velocity equation. You do not know the acceleration of C; you need to reference O to C to find that acceleration.

Can we assume that the theta_dot/omega for the angular velocities is in the -k direction since the disk in the visual is turning clockwise or will that not matter too much in the end?

Writing the omega vector in either the +k or -k direction works. Math will take care of the sign. Many times you are not able to visualize the direction of rotation. I find it easier to always assume +k, and then I know that getting a "-" means CW.

Is it the correct conclusion to observe that the acceleration of point O is strictly in the i direction?

Point O travels on a straight path in the x-direction. Since the path is straight, there is no component of acceleration normal to the path. Here, y is normal to the path. Therefore, there is not y-component of acceleration for point O.

When solving for v_B in reference to point A, at this instant, can we assume that the direction of v_B is strictly in the j-direction? Or does v_B have an i and a j component?

Two responses.

One, never make assumptions in this class. If something not given in the problem statement is true, then you should be able to show that it is true.

Two, in this case, that would not be a wise decision. The velocity of B has both x- and y-components. Write a velocity equation between C and B, and you will see this.

Once I derive the velocity equations necessary to solve for angular velocity, how do I get around the fact that they have different reference frames? Can I put the components of Vb/a and Vb/o in the same equation?

I am confused about what r_B/O would be in vector form. Any help would be greatly appreciated:)

r_B/O is the vector that extends from point O to point B; that is, r_B/O = - R*i.

Thank you!

I followed what the hints above said, but it gave me 3 equations and 4 unknowns, and I'm not sure why. The only way I could think to reduce this to 3 unknowns would be if the angular velocity of the bar was equal to that of the disk, but several people have said that this is not the case.

My equations are for v_B/A, v_O/C, and v_B/O, and I am left with the unknowns being v_B, v_O, omaga_disk, and omega_bar. What am I missing here so I can solve the equations?

Recall that each of your vector equations has two components: x and y.

How do you find the acceleration of C?

Please refer to Chapter 2 of the lecture book. It shows you how to find the acceleration of a no-slip point.

It's found in the lecture book on page 91, Ac = Rw^2

For finding velocity, could you just have 2 equations where you write a velocity equation relating A and B, and a velocity equation relating B and C?

No, you need three equations as you have three unknowns, Vb as a vector, wd, and wl. Look at the hints for this homework and hopefully that helps!

Because vA is constant, can we assume that aA=0?

Point A is moving with a CONSTANT speed and along a STRAIGHT path, so, yes, the acceleration of A is zero. Had the path of A been curved, even with constant speed, a_A ≠ 0.

The problem says to write the answers in vectors, does this just mean finding the values of angular acceleration and velocity, and then adding a k_hat to the end of it?

Yes, that is what is being ask. Be sure to provide the correct sign on your final vector answer.

When writing the velocity of B with respect to O, would we use the omega of the bar or the omega of the disc? I thought it would be omega bar.

Same question for the acceleration of the B with respect to O. Would we use alpha and omega for the disk or the bar?

How should we define the j component of V_a? I defined it as negative since V_a points down but I know some people who defined it as positive.

When calculating out the acceleration vector at point O in reference to point C. I’m getting a positive j_hat value. But when looking at the animation there is only acceleration in the i_hat direction. I’ve checked my cross products and signs too many times and I still can’t figure out how I’m getting my answer. I feel as though there should be a negative j_hat value that will cancel out the a_C vector so that it become zero but it isn’t working out that way at all. Is there something I’m missing?

While the disk may be moving and accelerating in the positive i direction, you need to consider how O is considering with respect to C. It would help to keep track of where C is while O is moving using your fingers as references for C and O.

Do we need to define new variables for rB/A in order to give it x and y vectors instead of just using L?

rB/A = L*i

I seem to be getting 4 unknowns from the 3 equations I have. Vb, Wab, Vo, and Wdisk. I'm assuming I did something wrong. How are we supposed to setup our 3 equations so that we only have 3 unknowns?