I've identified the unit vectors e_r and e_theta, and have an expression for each of those.
e_r = cos(phi) i + sin(phi) j
e_theta = -sin(phi) i + cos(phi) j
But after that, I'm stuck. Any hint on where to go from here would be helpful.
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6 comments:
There are three key pieces of information that you are given:
* R = 2*phi
* v = 3 ft/sec
* v = constant
Using the first, you can write: R_dot = 2*phi_dot. Using this with the second you can find R_dot and phi_dot by writing the magnitude of velocity (speed) in terms of R_dot and phi_dot.
Using R_dot_dot = 2*phi_dot_dot, v_dot = a•e_t and the third point above, you can find R_dot_dot and phi_dot_dot.
Using the third point, you can write the magnitude of the acceleration in terms of only the centripetal component. That will give you rho.
so for finding R_dot_dot and phi_dot_dot does this mean that we can assume that our acceleration is equal to zero
No, that would not be a good assumption to make.
Recall that acceleration has two components: the tangential (rate of change of speed) and the normal (centripetal) components.
The problem statement gives us that the speed is a constant (rate of change of speed is zero). This leaves only the centripetal component of acceleration. The centripetal component is not zero since v is not equal to zero.
It seems that the components of velocity are in the e_phi direction, yet when evaluating the equation at phi = pi I am having trouble coming up with the correct answer. I also have my acceleration as being purely in the -e_r direction (+e_n) for point A. I believe I am using the appropriate equations...do you think you can direct me as to where I may have erred?
From the equation R = 2*phi we know that R_dot = 2*phi_dot. Therefore, if a component of v in the e_R direction (R_dot) exists, then so must be a component in the e_phi (R*phi_dot). Based on this, it is not possible for the velocity to be in the e_phi direction only.
On acceleration, it looks like you are saying that e_R = -e_n. That could be part of your problem. e_R points directly to the left (along line from the origin through A). e_n, on the other hand, is perpendicular to e_t. e_t, based on the above, has both e_R and e_phi components since it is in the same direction as velocity. Therefore, e_n must also have both e_R and e_phi components.
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