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10. A yo-yo is made by wrapping a 2-m long string around a 500-g 10-cm diameter uniform disk. The string is fastened to the ceiling, and the yo-yo is released. What is the tension in the string as the yo-yo falls?
D. 0.49N

The answer is B. How do I get this answer? I'm having trouble figuring out why tension would be less than (mg). Thank you in advance.

  • Physics -

    Tension = T

    force up = T
    force down = m g
    m g - T = m a

    torque = I * angular acceleration
    T * R = I alpha = I a/R
    but I for disk = (1/2) m R^2
    T R = (1/2) m R a
    T = (1/2) m a interesting :)
    m g - (1/2) m a = m a
    g = (3/2) a
    a = (2/3) g
    T = (1/2) m (2/3) g = (1/3) m g
    = (1/3)(0.5)(9.81)
    = 1.63 N or B

  • Physics -

    T-tension, M –torque,
    I = mR²/2 -moment of inertia of disc
    ε-angular acceleration

    T•R= M
    I•ε =M
    ε =a/R
    I•a/R = T•R,
    a=TR²/I= 2TR²/mR²=2T/m,
    m•2T/m = mg-T,
    T=mg/3 =0.5•9.8/3 = 1.63
    ANS: B

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