Rotational Motion

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, $${{{F_1}} \over {{F_2}}}\,$$ 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

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 center is

An electric dipole is formed by two equal and opposite charges q with separation d. The charges have same mass m. It is kept in a uniform electric field E. If it is slightly rotated from its equilibrium orientation, then its angular frequency $$\omega$$ is :-

Initial angular velocity of a circular disc of mass $$M$$ is $${\omega _1}.$$ Then two small spheres of mass $$m$$ are attached gently to diametrically opposite points on the edge of the disc. What is the final angular velocity of the disc?

A particle performing uniform circular motion has angular frequency is doubled & its kinetic energy halved, then the new angular momentum is

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

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 $$\omega ' =$$

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

A thin horizontal circular disc is rotating about a vertical axis passing through its center. 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 the disc.

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 center of the hoop is zero. What will be the velocity of the center of the hoop when it cases to slip?

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 suspension:

A person of mass M is, sitting on a swing of length L and swinging with an angular amplitude $$\theta$$₀. If the person stands up when the swing passes through its lowest point, the work done by him, assuming that his center of mass moves by a distance $$\ell$$($$\ell$$ << L), is close to;

The time dependence of the position of a particle of mass m = 2 is given by $$\overrightarrow r \left( t \right) = 2t\widehat i - 3{t^2}\widehat j$$ . Its angular momentum, with respect to the origin, at time t = 2 is

A solid sphere of mass M and radius R is divided into two unequal parts. The first part has a mass of $${{7M} \over 8}$$ and is converted into a uniform disc of radius 2R. The second part is converted into a uniform solid sphere. Let I₁ be the moment of inertia of the disc about its axis and I₂ be the moment of inertia of the new sphere about its axis. The ratio I₁/I₂ is given by :

A thin smooth rod of length L and mass M is rotating freely with angular speed $$\omega$$₀ about an axis perpendicular to the rod and passing through its center. Two beads of mass m and negligible size are at the center of the rod initially. The beads are free to slide along the rod. The angular speed of the system , when the beads reach the opposite ends of the rod, will be :-

A solid sphere, a hollow sphere and a ring are released from top of an inclined plane (frictionless) so that they slide down the plane. Then maximum acceleration down the plane is for (no rolling)

If the angular momentum of a planet of mass m, moving around the Sun in a circular orbit is L, about the center of the Sun, its areal velocity is :

A wheel is rotating freely with an angular speed $$\omega$$ on a shaft. The moment of inertia of the wheel is I and the moment of inertia of the shaft is negligible. Another wheel of moment of inertia 3I initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is :