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Solving yo-yo problem using only energy equations - is this ok?

  1. Nov 12, 2011 #1
    1. The problem statement, all variables and given/known data

    A yo-yo has a rotational inertia of 960 gcm^2 and a mass of 120 g. Its axle radius is 3.2 mm and its string is 120 cm long. The yo-yo rolls from rest down to the end of the string. What is the magnitude of its linear acceleration?

    2. Relevant equations

    T - mg = ma

    3. The attempt at a solution

    I know there is an equation that specifically allows you to calculate the acceleration of the center of mass of a yo-yo, but I'm trying to figure it out without using that equation. I also see in the solution manual that the correct strategy is to analyze the forces acting on the yo-yo at the bottom, and then use torque expressions to find the Tension in terms of the acceleration and the radius of the axle.

    My question is just whether it's ok to solve this problem using energy equations instead of force equations. I took the following stab and seem to have arrived at a similar answer to the answer key. I just want to make sure this reasoning is sound, as I have found two answers to the problem so far and neither uses these energy equations.

    I set the problem up as follows, where v equals the linear velocity of the yo-yo, m equals the mass of the yo-yo, h is the length of the string, and r is the radius of its axle:

    Initial Energy of System = Final Energy of System

    (m)(gravity)(h) = 1/2(m)(v^2) + 1/2(I)(ω^2).

    (120 g)(980 cm/s^2)(120 cm) = 1/2(120 g)(v^2) + 1/2(950gcm^2)(v^2 / r^2)

    Solving this, I found that v=54.8 cm/s.

    I then plugged this into (final linear velocity)^2 = 2ah and found that a was 12.51 cm/s^2.

    Is this an ok approach?

  2. jcsd
  3. Nov 12, 2011 #2

    Doc Al

    User Avatar

    Staff: Mentor

    I didn't check your arithmetic, but your method is perfectly sound. Why not solve it using force equations to double check?
  4. Nov 12, 2011 #3
    Thanks! It seems to work!
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