Homework H.4.R

STEP 1 - FBD: The free body diagram of particle P shows only one force (the cable tension force), and this force always acts through the fixed point O.
STEP 2 - KINETICS: Above, you saw that all forces on P acted through the fixed point O - what does this say about the moments about point O and the consequences on the angular momentum about point O?
STEP 3 - KINEMATICS: The velocity of P is best written in terms of polar components: v = R_dot*e_R + R*φ_dot*e_φ. As discussed in class, you will not be able to calculate R_dot from the angular momentum equation. Recognizing this, you need to go back to STEP 2, and add on the work-energy equation for P. Question: How do you calculate the work done on P by the force F?
STEP 4 - SOLVE: At this point, you have a sufficient number of equations to solve for the two unknowns of R_dot and φ_dot.

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14 thoughts on “Homework H.4.R”

  1. Is the work due to the force F on the cable only accounted for in the work-energy equation? Is it safe to assume angular momentum is conserved from R1 - R2?

        1. GOPALAKH: As discussed in lecture, the angular momentum equation is not capable of giving us information on the radial component of velocity. If that component is needed, an additional equation is required. Typically, the work energy equation is useful in getting this additional equation.

    1. Yes, because the force from the string points directly towards the center, O. This makes it a 'central force' problem, which means angular momentum around the center does not change.

    1. The answer to this question is found by looking at the free body diagram (FBD) that you drew in Step 1. If this FBD shows no forces creating a moment about O, then you know that the summation of moments about O is zero. As a result, angular momentum is conserved about that point.

  2. I'm a bit confused on how to find the work in the work-energy equation. Should it just be F*deltaR? and do we need to take any angles into account if we have our coordinate system in polar coordinates?

    1. BLABELL and SARAH: Yes, the work is F*delta_R , where delta_R = R_1-R_2. Consider the motion of the end of the cable where the force is applied. The work is the force times the distance through which the end of the cable moves (which is delta_R).

      Make sense? If not, let us know.

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