System of Particles and Rotational Motion
In a carbon monoxide molecule, the carbon and the oxygen atoms are separated by a distance 1.2×10−10m. The distance of the centre of mass from the carbon atom is
Rod AB has length L. velocity of end A of the rod has velocity υ0 at the given instant.
(a). Which type of motion the rod has?
(b). Find velocity of end B at the given instant.
(C). Find the angular velocity of the rod.
A hoop of radius 2 m weighs 100 kg. It rolls along a horizontal floor so that its centre of mass has a speed of 20 cm/s. How much work has to be done to stop it?
Find the components along the x, y, z axes of the angular momentum l of a particle, whose position vector is r with components x, y, z and momentum is p with components px, py and pz. Show that if the particle moves only in the x-y plane the angular momentum has only a z-component.
A metre stick is balanced on a knife edge at its centre. When two coins, each of mass 5g are put one on one of the other at the 12cm mark, the stick is found to balanced at 45cm. The mass of the metre stick is.
Point A of rod AB(l=2m) is moved upwards against a wall with velocity v=2m/s. Find angular speed of the rod at an instant when θ=60∘.
Two discs of moments of inertia I1 and I2 about their respective axes (normal to the disc and passing through the centre), and rotating with angular speeds ω1 and ω2 are brought into contact face to face with their axes of rotation coincident. (a) What is the angular speed of the two-disc system? (b) Show that the kinetic energy of the combined system is less than the sum of the initial kinetic energies of the two discs. How do you account for this loss in energy? Take ω1 = ω2.
A uniform chain of length L and mass M is lying on a smooth table and one-third of its length is hanging vertically down over the edge of the table. If g is the acceleration due to gravity, the work required to pull the hanging part on to the table is