Define angular momentum.
Define angular momentum.
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A disc of mass $M$ and radius $R$ moves in the $x-y$ plane as shown in the figure. The angular momentum of the disc at the instant shown is
A disc of mass $M$ and radius $R$ moves in the $x-y$ plane as shown in the figure. The angular momentum of the disc at the instant shown is
A particle of mass $1 kg$ is subjected to a force which depends on the position as $\vec{F}=-k(x \hat{i}+y \hat{j}) kgms ^{-2}$ with $k=1 kgs ^{-2}$. At time $t=0$, the particle's position $\vec{r}=\left(\frac{1}{\sqrt{2}} \hat{i}+\sqrt{2} \hat{j}\right) m$ and its velocity $\vec{v}=\left(-\sqrt{2} \hat{i}+\sqrt{2} \hat{j}+\frac{2}{\pi} \hat{k}\right) m s^{-1}$. Let $v_x$ and $v_y$ denote the $x$ and the $y$ components of the particle's velocity, respectively. Ignore gravity. When $z=0.5 m$, the value of $\left(x v_y-y v_x\right)$ is. . . . . $m^2 s^{-1}$
A particle of mass $1 kg$ is subjected to a force which depends on the position as $\vec{F}=-k(x \hat{i}+y \hat{j}) kgms ^{-2}$ with $k=1 kgs ^{-2}$. At time $t=0$, the particle's position $\vec{r}=\left(\frac{1}{\sqrt{2}} \hat{i}+\sqrt{2} \hat{j}\right) m$ and its velocity $\vec{v}=\left(-\sqrt{2} \hat{i}+\sqrt{2} \hat{j}+\frac{2}{\pi} \hat{k}\right) m s^{-1}$. Let $v_x$ and $v_y$ denote the $x$ and the $y$ components of the particle's velocity, respectively. Ignore gravity. When $z=0.5 m$, the value of $\left(x v_y-y v_x\right)$ is. . . . . $m^2 s^{-1}$
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Two particles, each of mass $m$ and speed $v$, travel in opposite directions along parallel lines separated by a distance $d$. Show that the angular momentum vector of the two particle system is the same whatever be the point about which the angular momentum is taken.
Two particles, each of mass $m$ and speed $v$, travel in opposite directions along parallel lines separated by a distance $d$. Show that the angular momentum vector of the two particle system is the same whatever be the point about which the angular momentum is taken.
A $bob$ of mass $m$ attached to an inextensible string of length $l$ is suspended from a vertical support. The $bob$ rotates in a horizontal circle with an angular speed $\omega\, rad/s$ about the vertical. About the point of suspension
A $bob$ of mass $m$ attached to an inextensible string of length $l$ is suspended from a vertical support. The $bob$ rotates in a horizontal circle with an angular speed $\omega\, rad/s$ about the vertical. About the point of suspension
A fan of moment of inertia $0.6\,kg \times m^2$ is turned upto a working speed of $0.5$ revolutions per second. The angular momentum of the fan is
A fan of moment of inertia $0.6\,kg \times m^2$ is turned upto a working speed of $0.5$ revolutions per second. The angular momentum of the fan is