A disc of mass m and radius R is rolling without slipping on a horizontal- fixed rough surface with translational velocity v as shown in the figure- Here- LO and LP represent the angular momentum about point O and P respectively- Which of the following is-are true-

L_any point amp;=L_of CM about that point+L_about CM L⃗_O amp;=mvR ( k̂)+Iω ( k̂) amp;= mvRk̂ 1/2(mR^2)(v / R) k̂ amp;= mvRk̂ 1/2mvRk̂ amp;= 3/2m ...

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Byju's Answer

Standard X

Physics

Centripetal Force

A disc of mas...

Question

A disc of mass $m$ and radius $R$ is rolling without slipping on a horizontal, fixed rough surface with translational velocity $v$ as shown in the figure. Here, ${\to L}_{O} and {\to L}_{P}$ represent the angular momentum about point $O$ and $P$ respectively. Which of the following is/are true?

{\to L}_{O} = \frac{3}{2} mvR (-^k)

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{\to L}_{p} = \frac{1}{2} mvR (-^k)

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{\to L}_{O} = \frac{3}{2} m v R (^k)

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{\to L}_{p} = m v R (-^k)

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Solution

The correct option is D ${\to L}_{p} = m v R (-^k)$
$\begin{matrix} {\to L}_{any point} & = {\to L}_{of CM about that point} + {\to L}_{about CM} \end{matrix}$
$\begin{matrix} {\to L}_{O} & = mvR (-^k) + I ω (-^k) = - m v R^k - \frac{1}{2} ({m R}^{2}) (v / R)^k = - m v R^k - \frac{1}{2} m v R^k = - \frac{3}{2} m v R^k \end{matrix}$
$\begin{matrix} \to L p & = - m v \frac{R}{2}^k - I ω^k = - m v \frac{R}{2}^k - \frac{1}{2} m v R^k = - m v R^k \end{matrix}$

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A disc of mass m and radius R is rolling without slipping on a horizontal, fixed rough surface with translational velocity v as shown in the figure. Here, →LO and →LP represent the angular momentum about point O and P respectively. Which of the following is/are true?

The correct option is D →Lp=mvR(−^k)→Lany point =→Lof CM about that point+→Labout CM →LO=mvR(−^k)+Iω(−^k)=−mvR^k−12(mR2)(v/R)^k=−mvR^k−12mvR^k=−32mvR^k →Lp=−mvR2^k−Iω^k=−mvR2^k−12mvR^k=−mvR^k

A disc of mass $m$ and radius $R$ is rolling without slipping on a horizontal, fixed rough surface with translational velocity $v$ as shown in the figure. Here, ${\to L}_{O} and {\to L}_{P}$ represent the angular momentum about point $O$ and $P$ respectively. Which of the following is/are true?