Rotational Motion

The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through

A small mass attached to a string rotates on frictionless table top as shown. If the tension is the string is increased by pulling the string causing the radius of the circular motion to decrease by a factor of 2 , the…

From a disc of radius $R$ and mass $M$, a circular hole of diameter $R$, whose rim passes through the centre is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis, passing…

A heavy iron bar of weight $12\mathrm{kg}$ is having its one end on the ground and the other on the shoulder of a man. The rod makes an angle $60^{\circ}$ with the horizontal, the normal forceappliedby the man on baris:

A hoop of radius $\text{r}$ and mass $\text{m}$ rotating with an angular velocity $\omega\,_{0}$ is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity…

Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l.$ The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system (see…

Three solid spheres each of mass $m$ and diameter $d$ are stuck together such that the lines connecting the centres form an equilateral triangle of side of length $d$ . The ratio $\frac{I_{0}}{I_{A}}$ of moment of…

A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights $h_{sph}$ and $h_{cyl}$ on…

A huge circular arc of length $4.4\mathrm{ly}$ subtends an angle $4s$ at the centre of the circle. How long it would take for a body to complete $4$ revolution if its speed is $8\mathrm{AU}$ per second? Given :…

A uniform rod of length ' $\ell^{'}$is pivoted at one of its ends on a vertical shaft of negligible radius. When the shaft rotates at angular speed $\omega\,$ the rod makes an angle $\theta\,$with it (see figure). To…

A bob of mass m attached to an inextensible string of length $l$is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed $\omega\,$rad/s about the vertical. About the point of…

A sphere of mass $2\mathrm{kg}$ and radius $0.5m$ is rolling with an initial speed of $1ms^{-1}$ goes up an inclined plane which makes an angle of $30^{\circ}$ with the horizontal plane, without slipping. How low will…