Chapter 11 – Rotational Mechanics

A thin rod of length L and mass M is bent at its midpoint into two halves so that the angle between them is 90. The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is [...]

Four identical thin rods each of mass M and length l, form a square frame. Moment of inertia of this frame about an axis through the center of the square and perpendicular to its plane is : form a square frame. Moment of inertia of this frame about an axis through the center of the [...]

The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its mid-point and perpendicular to its length is I0. Its moment of inertia about an axis passing through one of its ends perpendicular to its length is. a circular hole of diameter R From a [...]

Point masses m1​ and m2​ are placed at the opposite ends of a rigid rod of length L, and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point P on this rod through which the axis should pass so that the work required to set [...]

Three identical spherical shells, each of mass m and radius r are placed as shown in figure. Consider an axis XX’ which is touching to two shells and passing through diameter of third shell. Moment of inertia of the system consisting of these three spherical shells about XX’ axis is a circular hole of diameter [...]

A light rod of length l has two masses m1​ and m2​ attached to its two ends. The moment of inertia of the system about an axis perpendicular to the rod and passing through the centre of mass is A light rod of length l has two masses m1​ and m2​ attached to its two [...]

A solid sphere of mass m and radius R is rotating about its diameter. A solid cylinder of the same mass and same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic energies of rotation (Esphere/Ecylinder) will be. a circular hole of [...]

Two rotating bodies A and B of masses m and 2m with moments of inertia IA​ and IB​ (IB​ IA​) have equal kinetic energy of rotation. If LA​ and LB​ be their angular moment a respectively, then: then Two rotating bodies A and B of masses m and 2m with moments of inertia IA​ and [...]

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 through the centre? a circular hole of diameter R From a disc of radius [...]

A particle of mass m moves in the XY plane with a velocity v along the straight line AB. If the angular momentum of the particle with respect to origin O is LA​ when it is at A and LB​ when it is at B, then : A particle of mass m moves in the [...]