Homework H6.A - Fa22

Problem statement
Solution video

DISCUSSION THREAD

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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 = +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.

 

4 thoughts on “Homework H6.A - Fa22”

  1. 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.

    1. 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.

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