Rotational Motion

The torque of a force $5 \hat{i}+3 \hat{j}-7 \hat{k}$ about the origin is $\tau$. If the force acts on a particle whose position vector is $2 \hat{i}+2 \hat{j}+\hat{k}$, then the value of $\tau$ will be :

A solid sphere of $80 \mathrm{~kg}$ and radius $15 \mathrm{~m}$ moving in a space becomes a circular disc of radius $20 \mathrm{~m}$ in $1 \mathrm{~h}$. The rate of change of moment of Inertia in this process is

A round disc of moment of inertia $\mathrm{I}_{2}$ about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia $\mathrm{I}_{1}$ rotating with an angular…

A solid cylinder and a hollow cylinder both of the same mass and same external diameter are released from the same height at the same time on an inclined plane. Both roll down without slipping. Which one will reach the…

A semicircular disc of mass $M$ and radius $R$ is free to rotate about its diameter. The moment of inertia of semicircular disc about a line perpendicular to its plane through centre is

A pulley of radius $2 m$ is rotated about its axis by a force $=(20t-5{t}^{2})$ newton (where $t$ is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is $10…

If the time period is doubled, then the angular momentum of the body will (provided the moment of inertia of the body is constant)

A circular disc of radius $\mathrm{R}$ and thickness $\frac{R}{6}$ has moment inertia I about an axis passing through its centre perpendicular to its plane. It is melted and recasted into a solid sphere. The moment of…

What is the moment of inertia of a solid sphere of density $\rho$ and radius $\mathrm{R}$ about its diameter?

A constant torque of $31.4 \mathrm{~N}-\mathrm{m}$ is exerted on a pivoted wheel. If angular acceleration of wheel is $4 \pi \mathrm{rad} / \mathrm{s}^{2},$ then the moment of inertia of the wheel is

The ratio of the accelerations for a solid sphere (mass 'm' and radius 'R') rolling down an incline of angle ' $\theta$ ' without slipping and slipping down the incline without rolling is:

The moment of inertia of a cube of mass $m$ and side $a$ about one of its edges is equal to