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Mar 5, 2008

Homework Hint: Problem 3/241


  • FBD: When you draw the FBD of particle P, you should observe that the z-component of the moment about point O is zero. Therefore, you should conclude that the z-component of the angular momentum about point O is a constant.
  • ANGULAR MOMENTUM EQUATION: The angular momentum of P about O is defined as: H_O = m r_P/O x v_P.
  • KINEMATICS: It is recommended that you write both r_P/O and v_P in terms of the polar unit vectors given above. Note that since b is a constant at both the beginning and at the end, you have R_dot = z_dot = 0 at both times 1 and 2. (This is not true in general; this is just a consequence of how the author wrote the problem.)
  • SOLVE: Use the conservation of angular momentum equation above to find omega_2.
  • The work term can be found directly from the work-energy equation since you will know the KE and PE of P at the beginning and end after finding omega_2 above.
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3 comments:

Brobe said...

What does the FBD consist of? A normal force, a tension force and gravitational force, is what I have, but since there is no z-axis moment about O then any force in the z direction(part of teh normal force and all of the gravitational force) is taken to as zero?

March 6, 2008 at 2:24 PM
CMK said...

It is correct that a summation of forces in the z-direction:

F_z = -mg + N*cos(30) + T*sin(30)

is zero at the beginning and end states since z is a constant then. At intermediate states, this is not true. However, this is really not an issue since a non-zero F_z does not contribute to the moment about the z-axis (a force in the z-direction cannot cause a moment about the z-axis).

Does this help in answering your question??

March 6, 2008 at 4:34 PM
Brobe said...

Yes, thanks. I just wanted to make sure I was understanding. I figured out the problem.

March 6, 2008 at 5:21 PM

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