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Newton's Second Law in Rotational Form

AP Physics 1· difficulty 4/5

m1 m2 M, R

Two blocks m1=2 kgm_1 = 2\text{ kg} and m2=3 kgm_2 = 3\text{ kg} hang on a string over a uniform-disk pulley of mass M=2 kgM = 2\text{ kg} and radius RR. What is the magnitude of acceleration? (Use g=10 m/s2g = 10\text{ m/s}^2.)

  • A

    2.0 m/s22.0\text{ m/s}^2

  • B

    3.0 m/s23.0\text{ m/s}^2

  • C

    1.0 m/s21.0\text{ m/s}^2

  • D

    106 m/s2≈1.67 m/s2\tfrac{10}{6}\text{ m/s}^2 \approx 1.67\text{ m/s}^2

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Explanation

With pulley moment of inertia I=12MR2I = \tfrac{1}{2}MR^2, a=(m2−m1)gm1+m2+M/2=(1)(10)2+3+1=106 m/s2a = \dfrac{(m_2 - m_1)g}{m_1 + m_2 + M/2} = \dfrac{(1)(10)}{2 + 3 + 1} = \tfrac{10}{6}\text{ m/s}^2.

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