Calculate the minimum amount of work necessary to overturn a crate of mass $100 \ kg$,first about edge $AB$,then about edge $A_1B_1$. The dimensions of the crate are given in the figure. (Assume $g = 10 \ m/s^2$) (in $J$)

$A$ thin rod $AB$ is sliding between two fixed right-angled surfaces. At some instant,its angular velocity is $\omega$. If $I_X$ represents the moment of inertia of the rod about an axis perpendicular to the plane and passing through the point $X$ ($A, B, C,$ or $D$),the kinetic energy of the rod is:

$A$ ladder of length $L$ is slipping with its ends against a vertical wall and a horizontal floor. At a certain moment,the speed of the end in contact with the horizontal floor is $v$ and the ladder makes an angle $\alpha = 30^o$ with the horizontal. Then the speed of the ladder's center must be

$A$ disc is rolling (without slipping) on a horizontal surface. $C$ is its center and $Q$ and $P$ are two points on the disc such that $Q$ is further from the contact point $O$ than $C$,and $P$ is closer to the contact point $O$ than $C$. Let $V_P, V_Q$ and $V_C$ be the magnitudes of the velocities of points $P, Q$ and $C$ respectively,then:

An equilateral prism of mass $m$ rests on a rough horizontal surface with coefficient of friction $\mu$. A horizontal force $F$ is applied on the prism at the top vertex $A$ as shown in the figure. If the coefficient of friction is sufficiently high so that the prism does not slide before toppling, then the minimum force required to topple the prism is $-$

$A$ disc rolls on a horizontal surface (without slipping). $C$ is the center and $Q$ and $P$ are two points at the same distance from $C$. Let $v_P$,$v_Q$,and $v_C$ be the magnitudes of the velocities of points $P$,$Q$,and $C$ respectively. Then: