Horizontal force $F_0$ is applied on a uniform circular disc of mass $M$ and radius $R$ which can rotate in vertical $x-y$ plane about an axes passing through $O$ as shown. What is the acceleration of bottom most point $P$ on the disc at this instant?

Consider the shown diagram. A fixed vertical smooth rod $AB$ is kept in front of a uniform disc of mass $m$ and radius $R$ which is rolling without slipping on a rough horizontal surface. Velocity of centre of disc is $\sqrt{3} \mathrm{m} {\mathrm{s}}^{-1}$. A rod $PQ$ of length $2 \mathrm{m}$ is connected with disc at $Q$, (point $Q$ is at a vertical distance of $\frac{R}{2}$ from centre of disc) by pin joint and other end of rod $PQ$ can freely slide over smooth vertical rod $AB$. At this instant rod $PQ$ makes an angle $\theta =150°$ with rod $AB$ as shown. Find the angular velocity of rod at this instant.

A uniform circular disc of mass $M\left(=1\mathrm{kg}\right)$ and radius $R\left(=1m\right)$ is fixed to vertical axis $AB$ with the help of a rod of length $L$ as shown. The disc rolls on a horizontal surface and is free to rotate about its centre. If there is no slipping at the point of contact of disc and horizontal surface then kinetic energy of the disc will be (given ${\omega }_0=2\mathrm{rad} {\mathrm{s}}^{-1}, L=1 \mathrm{m}$)

A uniform circular disc of mass $M$ and radius $R$ is having a point mass $M$ at its circumference is performing rolling without slipping over a rough horizontal surface as shown. Acceleration of point $O$ is $a_0$ towards right. If $N$ is the normal reaction on disc by the horizontal surface at this instant then

A rod of mass $\mathrm{m}$ and length $L$ is pivoted at the bottommost point $O$ and can freely rotate about the point $O$. The rod is disturbed from the vertical position so that it starts rotating about $O$. When it makes an angle $\theta$ with the vertical

A uniform rod of mass $5 \mathrm{m}$ and length $L$ is placed over a smooth horizontal surface. A particle of mass $m$ moving horizontally with velocity $v_0$ hits the rod at one end perpendicularly as shown in figure and comes to rest. Then

Statement-I: If there is no external torque on a body about its centre of mass, then the velocity of the centre of mass remains constant.

Statement-2: The linear momentum of an isolated system remains constant.