Consider a particle of mass $m$ having linear momentum $\vec p$ at position $\vec r$ relative to the origin $O$ . Let $\vec L$ be the angular momentum of the particle with respect the origin. Which of the following equations correctly relate $(s)\, \vec r,\,\vec p$ and $\vec L$ ?
Consider a particle of mass $m$ having linear momentum $\vec p$ at position $\vec r$ relative to the origin $O$ . Let $\vec L$ be the angular momentum of the particle with respect the origin. Which of the following equations correctly relate $(s)\, \vec r,\,\vec p$ and $\vec L$ ?
- A
$\frac{{d\vec L}}{{dt}} + \vec r\, \times \frac{{\overrightarrow {dp} }}{{dt}} = 0$
- B
$\frac{{d\vec L}}{{dt}}\, + \,\frac{{\overrightarrow {dr} }}{{dt}} \times \vec p = 0$
- C
$\frac{{d\vec L}}{{dt}}\, - \,\frac{{\overrightarrow {dr} }}{{dt}} \times \vec p = 0$
- D
$\frac{{d\vec L}}{{dt}}\, - \vec r \times \frac{{\overrightarrow {dp} }}{{dt}} = 0$
Similar Questions
A particle of mass $m$ is moving along the side of a square of side '$a$', with a uniform speed $v$ in the $x-y$ plane as shown in the figure
Which of the following statement is false for the angular momentum $\vec L$ about the origin ?
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The potential energy of a particle of mass $m$ at a distance $r$ from a fixed point $O$ is given by $\mathrm{V}(\mathrm{r})=\mathrm{kr}^2 / 2$, where $\mathrm{k}$ is a positive constant of appropriate dimensions. This particle is moving in a circular orbit of radius $\mathrm{R}$ about the point $\mathrm{O}$. If $\mathrm{v}$ is the speed of the particle and $\mathrm{L}$ is the magnitude of its angular momentum about $\mathrm{O}$, which of the following statements is (are) true?
$(A)$ $v=\sqrt{\frac{k}{2 m}} R$
$(B)$ $v=\sqrt{\frac{k}{m}} R$
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The potential energy of a particle of mass $m$ at a distance $r$ from a fixed point $O$ is given by $\mathrm{V}(\mathrm{r})=\mathrm{kr}^2 / 2$, where $\mathrm{k}$ is a positive constant of appropriate dimensions. This particle is moving in a circular orbit of radius $\mathrm{R}$ about the point $\mathrm{O}$. If $\mathrm{v}$ is the speed of the particle and $\mathrm{L}$ is the magnitude of its angular momentum about $\mathrm{O}$, which of the following statements is (are) true?
$(A)$ $v=\sqrt{\frac{k}{2 m}} R$
$(B)$ $v=\sqrt{\frac{k}{m}} R$
$(C)$ $\mathrm{L}=\sqrt{\mathrm{mk}} \mathrm{R}^2$
$(D)$ $\mathrm{L}=\sqrt{\frac{\mathrm{mk}}{2}} \mathrm{R}^2$
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