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