What is combined translation and rotation motion ? 

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Two hollow spheres each of mass $M$ and radius $\frac {R}{2}$ are connected with a massless rod of length $2R$ as shown in figure. What will be the moment of inhertia of the system about an axis $yy'$ passing through the center of one of the sphere and perpendicular to the rod

For the given figure find the acceleration of $1\, kg$ block if string is massless and mass of the pulley is $2\, kg$ and diameter of puller is $0.2\, m$ (in $m / s ^{2}$)

  • [AIIMS 2019]

Let $\mathop A\limits^ \to  $ be a unit vector along the axis of rotation of a purely rotating body and $\mathop B\limits^ \to  $ be a unit vector along the velocity of a particle $ P$ of the body away from the axis. The value of $\mathop A\limits^ \to  .\mathop B\limits^ \to  $ is

What do you mean by mass element $dm$ ? 

Two particles of equal mass are connected to a rope $AB$ of negligible mass such that one is at end $A$ and other dividing the length of rope in the ratio $1:2$ from $B$. The rope is rotated about end $B$ in a horizontal plane. Ratio of tensions in the smaller part to the other is (ignore effect of gravity)