Problem statementSolution video |

**DISCUSSION THREAD**

Any questions??

**Four-step plan**

**Step 1: FBD**

Draw a free-body diagram for the disk.

**Step 2: Kinetics - Work/energy**

Write down the kinetic energy and potential energy expressions for the disk, along with the work done on the disk by non-conservative forces. Note that point C is the instant center (zero velocity point) for the disk. Because of this, you are able to write down the KE for the disk as *T _{disk} = 0.5*I_{C}ω^{2}*, if you choose to do so. The work done by

*F*is equal to

*U = Fs*where

_{A},*s*is the distance traveled by end A of the cable.

_{A}* Step 3: Kinematics*Here you need to relate the distance traveled by point O to the distance traveled by end A of the cable (these are not the same). In doing this, recall that C is the instant center of the disk as it rolls without slipping.

**Step 4: Solve**

Solve your equations from Steps 2 and 3 for the speed of point O.

In order to relate O to A, can we consider them to be on the same rigid body? How else could we relate them?

Assuming you mean relating it for velocity, you can use C as the Instant Center and measure both the velocity of O, and then the point directly above O, which will be equal to the velocity of A.

I think they meant how do you solve for the distance that A travels, not the speed.

Once you find the relationship between the velocity of O and the velocity of A, you can integrate that equation to find the change in the distance traveled. For example, if v_B = 2*v_A, then delta_s_B = 2*delta_s_A

How can you solve for the distance that point A travels in relation to O, and why are they not the same?

Do we start by finding the distance of point A to the center O or should we use C as instant center to find the distance and use that to find the velocity of A?

Since the disk starts at rest and the spring is upstretched does this means that T1 and V1 equal zero?

Do we leave our answer in terms of d? I still have d in my final equation

Nevermind I read over the d value

https://www.youtube.com/watch?v=ziM7z4uuVMs

This example problem was really helpful for me when solving this problem. It's a similar problem except instead of gravitational potential energy, we have spring potential energy.

In the solution video, why was (1/2)mv^2 left out of the final equation (step 4)?