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Conservation of Angular Momentum

AP Physics 1· difficulty 4/5

I1, ω1 I2, drops

A disk with moment of inertia I1=4 kg⋅m2I_1 = 4\text{ kg·m}^2 rotates at ω1=6 rad/s\omega_1 = 6\text{ rad/s} about a vertical axis. A nonrotating disk with I2=2 kg⋅m2I_2 = 2\text{ kg·m}^2 is dropped onto it and they couple. What is the final angular speed?

  • A

    6 rad/s6\text{ rad/s}

  • B

    2 rad/s2\text{ rad/s}

  • C

    4 rad/s4\text{ rad/s}

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  • D

    3 rad/s3\text{ rad/s}

Explanation

Conserve angular momentum: I1ω1=(I1+I2)ωfI_1\omega_1 = (I_1 + I_2)\omega_f, so ωf=(4)(6)/6=4 rad/s\omega_f = (4)(6)/6 = 4\text{ rad/s}.

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