Chapter 6 – System of Particles and Rotational Motion

To maintain a rotor at a uniform angular speed of 200 rad s^−1 , an engine needs to transmit a torque of 180 N m. What is the power required by the engine ? (Note: uniform angular velocity in the absence of friction implies zero torque. In practice, applied torque is needed to counter frictional [...]

A rope of negligible mass is wound round a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N? What is the linear acceleration of the rope ? Assuming that there is no slipping. find its [...]

(a) A child stands at the centre of a turntable with his two arms outstretched. The turntable is set rotating with an angular speed of 40 rev/min. How much is the angular speed of the child if he folds his hands back and thereby reduces his moment of inertia to 2/5 times the initial value [...]

A solid cylinder of mass 20 kg rotates about its axis with angular speed 100 rad s^−1. The radius of the cylinder is 0.25 m. What is the kinetic energy associated with the rotation of the cylinder? What is the magnitude of angular momentum of the cylinder about its axis? find its moment of inertia [...]

Torques of equal magnitude are applied to hollow cylinder and a solid sphere, both having the same mass and same radius. The cylinder is free to rotate about its standard axis of symmetry, and the sphere is free to rotate about an axis passing through its centre. which of the two will acquire a greater [...]

Given, moment of inertia of a disc of mass M and radius R about any of its diameters = mR^2/4, find its moment of inertia about an axis normal to the disc and passing through a point on its edge. find its moment of inertia about an axis normal to the disc and passing through [...]

Find the moment of inertia of a sphere about a tangent to the sphere, given the moment of inertia of the sphere about any of its diameters to be 2MR^2/5, where M is the mass of the sphere and R is the radius of the sphere. Find the moment of inertia of a sphere about [...]

A car weighs 1800 kg. The distance between its front and back axles is 1.8 m. Its centre of gravity is 1.05 m behind the front axle. Determine the force exerted by the level ground on each front wheel and each back wheel. given that a chlorine atom is about 35.5 times as massive as [...]

A non-uniform bar of weight W is suspended at rest by two strings of negligible weight as shown in Fig. The angles made by the strings with the vertical are 36.9^∘ and 53.1^∘ respectively. The bar is 2m long. Calculate the distance d of the centre of gravity of the bar from its left end. [...]

A child sits stationary at one end of a long trolley moving uniformly with a speed V on a smooth horizontal floor. If the child gets up and runs about on the trolley in any manner what is the speed of the centre of mass of the trolley + child system? given that a chlorine [...]