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Newton's Second Law in Rotational Form

AP Physics 1· difficulty 4/5

F R

A uniform disk of mass M=4 kgM = 4\text{ kg} and radius R=0.5 mR = 0.5\text{ m} is free to rotate about its center. A constant tangential force F=10 NF = 10\text{ N} is applied at the rim. What is the angular acceleration?

  • A

    2.5 rad/s22.5\text{ rad/s}^2

  • B

    20 rad/s220\text{ rad/s}^2

  • C

    5 rad/s25\text{ rad/s}^2

  • D

    10 rad/s210\text{ rad/s}^2

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Explanation

τ=FR\tau = FR and I=12MR2I = \tfrac{1}{2}MR^2, so α=τ/I=2F/(MR)=(2)(10)/(4⋅0.5)=10 rad/s2\alpha = \tau/I = 2F/(MR) = (2)(10)/(4 \cdot 0.5) = 10\text{ rad/s}^2.

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