Homework H5.D - Fa22

DISCUSSION: Four-step plan

Step 1: FBD
Draw individual free-body diagrams for the drum and block.

Step 2: Kinetics - Newton/Euler
Write down the Newton/Euler equations for the drum. Note that since the drum does not slip on either cable, point C on the drum is the instant center for the drum, with the acceleration of C, therefore, pointing toward the center of mass O. Because of this, you are able to use C for your Euler (moment) equation. This will simplify your analysis. Please note that if you do use C, you will need to use the parallel axis theorem in finding the mass moment of inertia of the drum about C.

Step 3: Kinematics
Use the fact that C is the center of rotation  in relating the kinematics of the drum to the kinematics of block B. Be careful in abiding by your sign conventions in this step. That is, if you chose the CCW direction to be positive for moments back in Step 2, this becomes the positive sign conventions for the angular acceleration. Similarly, if you chose the upward direction of B to be positive in the Newton equation for B, then that is the positive sign convention for the acceleration of block B.

Step 4: Solve
Solve your equations from Steps 3 and 4 for the angular acceleration of the drum and the acceleration of block B.

3 thoughts on “Homework H5.D - Fa22”

1. Enrico Setiawan says:

In the solution video for H5.D why is -T_B not included in the sum of Y-forces for the drum (2:10 in the video).

2. Lin says:

How do we know that C is the instant center in this case? It's not immediately obvious to me. Are there any tricks for finding them for these types of problems?

1. Enrico Setiawan says:

The drum rolls without slipping on the cable, and the instant center will always be the point of contact between the surface (cable in this case) and the disk (drum). You can also verify this by knowing that V_o is traveling up, and a perpendicular line from its vector will intersect at C.