$A$ particle of mass $0.5\, kg$ is rotating in a circular path of radius $2m$ and centrepetal force on it is $9$ Newtons. Its angular momentum (in $J·sec$) is:
$A$ particle of mass $0.5\, kg$ is rotating in a circular path of radius $2m$ and centrepetal force on it is $9$ Newtons. Its angular momentum (in $J·sec$) is:
- A
$1.5$
- B
$3$
- C
$6$
- D
$18$
Similar Questions
A binary star consists of two stars $\mathrm{A}$ (mass $2.2 \mathrm{M}_5$ ) and $\mathrm{B}$ (mass $11 \mathrm{M}_5$ ), where $\mathrm{M}_5$ is the mass of the sun. They are separated by distance $\mathrm{d}$ and are rotating about their centre of mass, which is stationary. The ratio of the total angular momentum of the binary star $\mathrm{A}$ to the angular momentum of star $\mathrm{B}$ about the centre of mass is
A binary star consists of two stars $\mathrm{A}$ (mass $2.2 \mathrm{M}_5$ ) and $\mathrm{B}$ (mass $11 \mathrm{M}_5$ ), where $\mathrm{M}_5$ is the mass of the sun. They are separated by distance $\mathrm{d}$ and are rotating about their centre of mass, which is stationary. The ratio of the total angular momentum of the binary star $\mathrm{A}$ to the angular momentum of star $\mathrm{B}$ about the centre of mass is
- [IIT 2010]
Given $V _{ CM }=2\; m / s , m =2\; kg , R =4\; m $
Find angular momentum of ring about origin if it is in pure rolling. $kgm ^{2} / s$
Given $V _{ CM }=2\; m / s , m =2\; kg , R =4\; m $
Find angular momentum of ring about origin if it is in pure rolling. $kgm ^{2} / s$
- [AIIMS 2019]
A thin rod of mass $M$ and length $a$ is free to rotate in horizontal plane about a fixed vertical axis passing through point $O$. A thin circular disc of mass $M$ and of radius $a / 4$ is pivoted on this rod with its center at a distance $a / 4$ from the free end so that it can rotate freely about its vertical axis, as shown in the figure. Assume that both the rod and the disc have uniform density and they remain horizontal during the motion. An outside stationary observer finds the rod rotating with an angular velocity $\Omega$ and the disc rotating about its vertical axis with angular velocity $4 \Omega$. The total angular momentum of the system about the point $O$ is $\left(\frac{ M a^2 \Omega}{48}\right) n$. The value of $n$ is. . . . .
A thin rod of mass $M$ and length $a$ is free to rotate in horizontal plane about a fixed vertical axis passing through point $O$. A thin circular disc of mass $M$ and of radius $a / 4$ is pivoted on this rod with its center at a distance $a / 4$ from the free end so that it can rotate freely about its vertical axis, as shown in the figure. Assume that both the rod and the disc have uniform density and they remain horizontal during the motion. An outside stationary observer finds the rod rotating with an angular velocity $\Omega$ and the disc rotating about its vertical axis with angular velocity $4 \Omega$. The total angular momentum of the system about the point $O$ is $\left(\frac{ M a^2 \Omega}{48}\right) n$. The value of $n$ is. . . . .
- [IIT 2021]
Define angular momentum.
Define angular momentum.
A particle of mass $M=0.2 kg$ is initially at rest in the $x y$-plane at a point $( x =-l, y =-h)$, where $l=10 m$ and $h=1 m$. The particle is accelerated at time $t =0$ with a constant acceleration $a =10 m / s ^2$ along the positive $x$-direction. Its angular momentum and torque with respect to the origin, in SI units, are represented by $\vec{L}$ and $\vec{\tau}$, respectively. $\hat{i}, \hat{j}$ and $\hat{k}$ are unit vectors along the positive $x , y$ and $z$-directions, respectively. If $\hat{k}=\hat{i} \times \hat{j}$ then which of the following statement($s$) is(are) correct?
$(A)$ The particle arrives at the point $(x=l, y=-h)$ at time $t =2 s$.
$(B)$ $\vec{\tau}=2 \hat{ k }$ when the particle passes through the point $(x=l, y=-h)$
$(C)$ $\overrightarrow{ L }=4 \hat{ k }$ when the particle passes through the point $(x=l, y=-h)$
$(D)$ $\vec{\tau}=\hat{ k }$ when the particle passes through the point $(x=0, y=-h)$
A particle of mass $M=0.2 kg$ is initially at rest in the $x y$-plane at a point $( x =-l, y =-h)$, where $l=10 m$ and $h=1 m$. The particle is accelerated at time $t =0$ with a constant acceleration $a =10 m / s ^2$ along the positive $x$-direction. Its angular momentum and torque with respect to the origin, in SI units, are represented by $\vec{L}$ and $\vec{\tau}$, respectively. $\hat{i}, \hat{j}$ and $\hat{k}$ are unit vectors along the positive $x , y$ and $z$-directions, respectively. If $\hat{k}=\hat{i} \times \hat{j}$ then which of the following statement($s$) is(are) correct?
$(A)$ The particle arrives at the point $(x=l, y=-h)$ at time $t =2 s$.
$(B)$ $\vec{\tau}=2 \hat{ k }$ when the particle passes through the point $(x=l, y=-h)$
$(C)$ $\overrightarrow{ L }=4 \hat{ k }$ when the particle passes through the point $(x=l, y=-h)$
$(D)$ $\vec{\tau}=\hat{ k }$ when the particle passes through the point $(x=0, y=-h)$
- [IIT 2021]