Given v_ C M =2 ~m ~s^ -1 , m=2 ~kg, R=4 ~m Find the angular...

Given

v_{C M}=2 \mathrm{~m} \mathrm{~s}^{-1}

m=2 \mathrm{~kg}, R=4 \mathrm{~m}

Find the angular momentum of ring about its origin if it is in pure rolling. Given v_ C M =2 ~m ~s^ -1 , m=2 ~kg, R=4 ~m Find the angular momentum of ring about its origin if it is in pure rolling.

Given v_ C M =2 ~m ~s^ -1 , m=2 ~kg, R=4 ~m Find the angular momentum of ring about its origin if it is in pure rolling.

Options

A $32 \mathrm{~kg} \mathrm{~m}^2 \mathrm{~s}^{-1}$
B $24 \mathrm{~kg} \mathrm{~m}^2 \mathrm{~s}^{-1}$
C $16 \mathrm{~kg} \mathrm{~m}^2 \mathrm{~s}^{-1}$
D $8 \mathrm{~kg} \mathrm{~m}^2 \mathrm{~s}^{-1}$

Correct answer

A. $32 \mathrm{~kg} \mathrm{~m}^2 \mathrm{~s}^{-1}$

Step-by-step solution

\begin{aligned} & \text{ } \vec{L}=I_{C M} \cdot \omega+m v_{C M} R \\ & \omega=\frac{v}{R}=\frac{2}{4}=0.5 \mathrm{rad} \mathrm{s}^{-1} \\ & \vec{L}=m R^2 \cdot \omega+m v_{C M} \cdot R \\ & =2 \times 16 \times 0.5+2 \times 2 \times 4=16+16 \\ & \vec{L}=32 \mathrm{ kg} \mathrm{ m}^2 \mathrm{ s}^{-1}\end{aligned}

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