Rotational Motion

List-I shows four planar structures made of uniform solid rods each of mass $m$ and length $l$. In the List-II the possible moment of inertia of these structures about an axis $OCO'$, which lies in the plane of the…

A solid cylinder of radius $R$ rolls without slipping with a center of mass speed $v_0 = \sqrt{\dfrac{gR}{3}}$ on a horizontal surface with a vertical edge, as shown in the figure. Here, $g$ is the acceleration due to…

Consider a large disk of radius $R$ and two smaller disks, each of radius $r = R/50$, lying on its circumference, as shown in the figure. The smaller disks are initially in contact with each other, with an angular…

An annular disk of mass $M$, inner radius $a$ and outer radius $b$ is placed on a horizontal surface with coefficient of friction $\mu$, as shown in the figure. At some time, an impulse $J_{0}x\wedge$ is applied at a…

A flat surface of a thin uniform disk $A$ of radius $R$ is glued to a horizontal table. Another thin uniform disk $B$ of mass $M$ and with the same radius $R$ rolls without slipping on the circumference of $A$, as shown…

A particle of mass $M=0.2kg$ is initially at rest in the $xy$-plane at a point $(x=-l,y=-h)$, where $l=10m$ and $h=1m$. The particle is accelerated at time $t=0$ with a constant acceleration $a=10ms^{-2}$ along the…

A horizontal force $F$ is applied at the centre of mass of a cylindrical object of mass $m$ and radius $R$, perpendicular to its axis as shown in the figure. The coefficient of friction between the object and the ground…

A rod of mass $m$ and length $L,$ pivoted at one of its ends, is hanging vertically. A bullet of the same mass moving at speed $v$ strikes the rod horizontally at a distance $x$ from its pivoted end and gets embedded in…

A small roller of diameter $20cm$ has an axle of diameter $10cm$ (see figure below on the left). It is on a horizontal floor and a meter scale is positioned horizontally on its axle with one edge of the scale on top of…

A football of radius $R$ is kept on a hole of radius $r(rR)$ made on a plank kept horizontally. One end of the plank is now lifted so that it gets tilted making an angle $\theta$ from the horizontal as shown in the…

Paragraph: One twirls a circular ring (of mass $M$ and radius $R$) near the tip of one's finger as shown in Figure 1 . In the process the finger never loses contact with the inner rim of the ring. The finger traces out…

Paragraph: One twirls a circular ring (of mass $M$ and radius $R$ ) near the tip of one's finger as shown in Figure 1 . In the process the finger never loses contact with the inner rim of the ring. The finger traces out…