A particle of mass $m = 5$ is moving with a uniform speed $v = 3\sqrt 2$ in the $XOY$ plane along the line $Y = X + 4$ . The magnitude of the angular momentum of the particle about the origin is .......

A bullet of mass $10\, g$ and speed $500\, m/s$ is fired into a door and gets embedded exactly at the centre of the door. The door is $1.0\, m$ wide and weighs $12\, kg$. It is hinged at one end and rotates about a vertical axis practically without friction . The angular speed of the door just after the bullet embeds into it will be

$A$ hollow sphere of radius $R$ and mass $m$ is fully filled with water of mass $m$. It is rolled down a horizontal plane such that its centre of mass moves with a velocity $v$. If it purely rolls

A particle is moving along a straight line parallel to $x$-axis with constant velocity. Find angular momentum about the origin in vector form

A particle of mass $20\,g$ is released with an initial velocity $5\,m/s$ along the curve from the point $A,$ as shown in the figure. The point $A$ is at height $h$ from point $B.$ The particle slides along the frictionless surface. When the particle reaches point $B,$ its angular momentum about $O$ will be ......... $kg - m^2/s$. [Take $g = 10\,m/s^2$ ]

Obtain $\tau = I\alpha $ from angular momentum of rigid body.