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Newton's Second Law in Rotational Form

AP Physics 1· difficulty 3/5

A solid disk pulley of mass 4 kg4~\text{kg} and radius 0.20 m0.20~\text{m} has a string wrapped around it. A tension of 10 N10~\text{N} pulls the string. The angular acceleration of the disk (I=12MR2I = \tfrac{1}{2}M R^2) is

  • A

    2 rad/s22~\text{rad/s}^2

  • B

    50 rad/s250~\text{rad/s}^2

  • C

    25 rad/s225~\text{rad/s}^2

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  • D

    10 rad/s210~\text{rad/s}^2

Explanation

I=0.5(4)(0.04)=0.08 kg⋅m2I = 0.5 (4)(0.04) = 0.08~\text{kg·m}^2. τ=TR=(10)(0.20)=2.0 N⋅m\tau = T R = (10)(0.20) = 2.0~\text{N·m}. α=2.0/0.08=25 rad/s2\alpha = 2.0/0.08 = 25~\text{rad/s}^2.

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