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Conservation of Angular Momentum

AP Physics 1· difficulty 3/5

A disk (I=0.20 kg⋅m2I = 0.20~\text{kg·m}^2) spins at ω0=6 rad/s\omega_0 = 6~\text{rad/s}. A 0.50 kg0.50~\text{kg} putty falls onto its rim at r=0.30 mr = 0.30~\text{m} and sticks. New angular speed?

  • A

    4.2 rad/s4.2~\text{rad/s}

  • B

    6.0 rad/s6.0~\text{rad/s}

  • C

    4.9 rad/s4.9~\text{rad/s}

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  • D

    3.6 rad/s3.6~\text{rad/s}

Explanation

Inew=0.20+(0.50)(0.30)2=0.245I_\text{new} = 0.20 + (0.50)(0.30)^2 = 0.245. Conservation: ω=0.20(6)/0.245≈4.9 rad/s\omega = 0.20(6)/0.245 \approx 4.9~\text{rad/s}.

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