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Jan 16, 2008

Homework Hint: Problem 5/6


  • Recognize that O is a fixed point: a_O = 0.
  • Use the rigid body equation to relate the accelerations of O and P:  a_P = a_O + alpha x r_P/O + omega x (omega x r_P/O).
  • Use given information on the vector form of the acceleration of P, a_P.
  • Balance i and j components of acceleration equation.
  • Solve the two equations for the two unknowns: omega and alpha.
Note that the process to be used for solving Problem 5/18 is very similar to that used above for Problem 5/6. In Problem 5/18, use the relationship between omega and alpha to find t.

6 comments:

n.c.kempfert said...

This hint says to solve using the two equations. I am confused, what equation do I have aside from the one outlined in the hint?

CMK said...

The vector equation for the acceleration of point P has two components: x and y. This one vector equation therefore has two scalar equations (one for x and one for y). These are the two equations to which I refer.

Chris Cohoat said...

When solving for angular velocity, w, are we allowed to just have the positive result as our answer? This would make sense if we were not looking for a direction but just a magnitude, but I'm not sure. Thanks.

Chris Cohoat said...

I of course meant *since but there's no edit feature. Whoops.

CMK said...

Good question.

The radial component of the acceleration goes as omega^2. Therefore, that component is the same whether the disk is rotating CCW (positive) or CW (positive). Either direction works.

David Rojas said...

I dunno if i did this right but I just started with a = -a_t_i - a_n_j and just used the i and j components given and used them with the corresponding equations for a_n and a_t in the book