A particle of mass $m$ is projected at $45^o$ at $V_0$ speed from point $P$ at $t = 0$. The angular momnetum of particle about $P$ at $t = \frac{V_0}{g}$ is:-
$\frac{1}{2 \sqrt 2} \frac{mV_0^3}{g}$
$\frac{1}{2 \sqrt 2} \frac{mV_0^2}{g}$
$\frac{1}{2} \frac{mV_0^3}{g}$
$\frac{1}{2} \frac{mV_0^2}{g}$
The direction of the angular velocity vector along
A pendulum consists of a bob of mass $m=0.1 kg$ and a massless inextensible string of length $L=1.0 m$. It is suspended from a fixed point at height $H=0.9 m$ above a frictionless horizontal floor. Initially, the bob of the pendulum is lying on the floor at rest vertically below the point of suspension. A horizontal impulse $P=0.2 kg - m / s$ is imparted to the bob at some instant. After the bob slides for some distance, the string becomes taut and the bob lifts off the floor. The magnitude of the angular momentum of the pendulum about the point of suspension just before the bob lifts off is $J kg - m ^2 / s$. The kinetic energy of the pendulum just after the lift-off is $K$ Joules.
($1$) The value of $J$ is. . . . . .
($2$) The value of $K$ is. . . . .
Give the answers of the questions ($1$) and ($2$)
$A$ time varying force $F = 2t$ is applied on a spool rolling as shown in figure. The angular momentum of the spool at time $t$ about bottommost point is:
A ring of mass $M$ and radius $R$ is rotating with angular speed $\omega$ about a fixed vertical axis passing through its centre $O$ with two point masses each of mass $\frac{ M }{8}$ at rest at $O$. These masses can move radially outwards along two massless rods fixed on the ring as shown in the figure. At some instant the angular speed of the system is $\frac{8}{9} \omega$ and one of the masses is at a distance of $\frac{3}{5} R$ from $O$. At this instant the distance of the other mass from $O$ is
Angular momentum of a single particle moving with constant speed along circular path: