Problem statementSolution video |

**DISCUSSION THREAD**

Any questions?? Ask and answer questions in the discussion thread below.

**DISCUSSION**

**Four-step plan**

**Step 1: FBD**

Draw *individual* free-body diagrams for the collar A and the disk. Do not forget the friction force on the disk at C when drawing your FBD of the disk. Define a coordinate *x* that describes the motion of the disk center O. Let's say you choose *x* to be positive to the left. Be sure that the directions of the spring forces on the collar are consistent with your definition of *x*.

**Step 2: Kinetics - Newton/Euler**

Write down the Newton/Euler equations for the collar and the disk. Be sure to abide by the sign conventions defined for *θ* and *x *when writing down these equations.

* Step 3: Kinematics*The kinematics that you need here are to relate

*θ*and

*x*. Be reminded that the contact point C is the instant center for the disk. As before, be sure to abide by the sign conventions defined for

*θ*and

*x*. For x defined positive to the left and

*θ*defined positive

*CCW*, we have

*x*=

*+Rθ*

*.*

**Step 4: Equation of motion**

Combine your equations from Steps 2 and 3 to end up with the differential equation of motion for the system.

Is there any way to determine the initial motion of the disk prior to deriving an equation? I’m trying to put together a FBD and struggling to understand how this thing moves.

Also, is the initial motion of the device of any use to us? Or am I aproaching this problem the wrong way.

In the problem itself, theta is defined as positive in the anti-clockwise direction, so when drawing my FBD, I assumed that the disk also rotates in the anti-clockwise direction for ease of calculation. I guess you could instead assume that the disk rotates in the other way, as long as your calculations are consistent, but that might make things a little confusing.

I'm not really sure what the purpose of the collar is and how to include this into the problem. I just added the weight to the center of the disk so that there was no moment. Is this correct?

I am also confused what the purpose of the collar is. Do we have to include both collars in our system or does it not matter?