Rotational Mechanics — JEE Main PYQs

A mass 'm' is supported by a massless string wound around a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration will the mass fall on release?

A hoop of radius $r$ and mass $m$ 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 of the centre of the hoop when it ceases to slip?

A mass $m$ hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass $m$ and radius $R$. Assuming pulley to be a perfect uniform circular disc, the acceleration of the mass $m$, if the string does not slip on the pulley, is

A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, the angular speed of …

A pulley of radius 2 m is rotated about its axis by a force $F=\left(20t-5t^2\right)$ Newton (where $t$ is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is $10{\text{kg m}}^2$, the number of rotations made by th …

A small particle of mass $m$ is projected at an angle $\theta$ with the $x$-axis with an initial velocity ${\mathrm{v}}_0$ in the $\mathrm{x}-\mathrm{y}$ plane as shown in the figure. At a time $\mathrm{t}<\frac{{\mathrm{v}}_0\sin \theta }{\mathrm{g}}$, the angular momentum of t …

Consider a uniform square plate of side 'a' and mass 'm'. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is

A round uniform body of radius R, mass M and moment of inertia 'I', rolls down (without slipping) an inclined plane making an angle $\theta$ with the horizontal. Then its acceleration is

Angular momentum of the particle rotating with a central force is constant due to

For the given uniform square lamina ABCD, whose centre is O, which of the following is true? (E and F are the midpoints of AB and DC respectively.)

A force of $-\mathrm{F}\hat{\mathrm{k}}$ acts on O, the origin of the coordinate system. The torque about the point $(1,-1)$ is

A thin circular ring of mass $m$ and radius $R$ is rotating about its axis with a constant angular velocity $\omega$. Two objects each of mass M are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity ${\omega }^{\prime }=$

Four point masses, each of value m, are placed at the corners of a square ABCD of side $\ell$. The moment of inertia through A and parallel to BD is

An annular ring with inner and outer radii $R_1$ and $R_2$ is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring, $F_1/F_2$ is

The moment of inertia of a uniform semicircular disc of mass M and radius r about a line perpendicular to the plane of the disc through the centre is

A 'T' shaped object with dimensions shown in the figure, is lying on a smooth floor. A force $F$ is applied at the point P parallel to AB, such that the object has only the translational motion without rotation. Find the location of P with respect to C

A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which one of the following will not be affected?

One solid sphere A and another hollow sphere B are of same mass and same outer radii. Their moment of inertia about their diameters are respectively ${\mathrm{I}}_{\mathrm{A}}$ and ${\mathrm{I}}_{\mathrm{B}}$ such that

Where ${\mathrm{d}}_{\mathrm{A}}$ and ${\mathrm{d}}_{\mathrm{B}}$ ar …