$A$ table rotates about a vertical axis passing through its center with an angular velocity of $20\ rad/s$. $A$ flywheel is mounted on it,which rotates about a horizontal axis with an angular velocity of $40\ rad/s$. The resultant angular velocity of the flywheel is:

The moment of inertia of a solid flywheel about its axis is $0.1\,kg\cdot m^2$. $A$ tangential force of $2\,kg\cdot wt$ is applied around the circumference of the flywheel with the help of a string and mass arrangement as shown in the figure. If the radius of the wheel is $0.1\,m$,find the angular acceleration of the solid flywheel (in $rad/s^2$). (Take $g = 9.8\,m/s^2$)

$A$ uniform rod of mass $m$ and length $l$ rotates in a horizontal plane with an angular velocity $\omega$ about a vertical axis passing through one end. The tension in the rod at a distance $x$ from the axis is

What is a rigid body?

$A$ ring has inner radius $R_1$ and outer radius $R_2$. It rolls without slipping with a constant angular velocity $\omega$. What is the ratio of the forces $F_1/F_2$ experienced by two particles located on the inner and outer surfaces of the ring?

The linear velocity of a rotating body is given by $\overrightarrow v = \overrightarrow \omega \times \overrightarrow r,$ where $\overrightarrow \omega$ is the angular velocity and $\overrightarrow r$ is the radius vector. If the angular velocity of a body is $\overrightarrow \omega = \hat i - 2\hat j + 2\hat k$ and the radius vector is $\overrightarrow r = 4\hat j - 3\hat k,$ then find the magnitude of linear velocity $|\overrightarrow v |$.