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Apr 8, 2008

Homework Hints: Vib-3


  • FBDs: It is recommended that you draw individual FBDs for the drum and block. Choose a translational coordinate for the block; e.g., "y" measured positively downward. In drawing the FBD's, recall that the tension on both sides of the drum are NOT equal (due to the rotational inertia of the drum).
  • Newton-Euler: Use Newton in y-direction for the block. Use Euler for the drum.
  • Kinematics: Relate the translation of the block (y) to the rotation of the drum (theta).
  • EOM: Combine your two Newton-Euler equations with the kinematics to obtain a single differential equation of motion (EOM) for the system in terms of theta and its time derivatives.

3 comments:

Purdue FSAE said...

I wasn't sure how the kinematics worked on this one... I used Ydotdot=r*Thetadotdot, (kind of like a=r*alpha) with y measured mositively downwards in my FBD. I first don't know if/why this is the right equation, and if it is, how does the sign convention work for this one?

CMK said...

Yes, that is correct: y_dot_dot = r*theta_dot_dot (with y measured positively down and theta measured positively CCW)

The way to work this is to write out the kinematics equation between the center of the drum and the point where the cable comes off the drum on the left side. Both the magnitude and sign come directly from these kinematics.

To check the sign, a positive movement of the block (down) corresponds to a positive rotation of the drum (CCW).

Does that help?

Purdue FSAE said...

yes, that clears things up. thanks!