Question

1. Write an expression for the centre of mass of a two particle system. What will be the location of centre of mass if the two particles have equal masses? 2. Show that the total linear momentum of a system of particles is equal to the product of the total mass of the system and the velocity of its centre of mass. 3.Define the torque or moment of force. Give its units and dimensions. 4. State and explain the principle of moments. 5. Derive an expression of the work done by a torque. Hence, write the expression for the power delivered by a torque. 5. Prove that the time rate of change of the angular momentum of a particle is equal to the torque acting on it. 5. Define moment of inertia of a body. Give its units and dimensions. What is the physical significance of moment of inertia? 6. Derive an expression for the rotational kinetic energy of a body and hence define moment of inertia. 9. Define radius of gyration. What is its physical significance? 10. State and prove that theorem of perpendicular axis on moment of inertia. 11 . State and prove the theorem of parallel axes on moment of inertia. 12: State the law of conservation of angular momentum and illustrate it with the example of planetary motion. 13. A body is rotating with uniform angular velocity w about an axis. Establish the formula of its.kinetic energy of-rotation. 13. Derive the three equations of rotational motion and the constant angular acceleration from first principles.

Answer 1

×1+x2/2,y1+y2/2
summation of p= summationof m×v cm
torque is the product of f and perpendicular distance of f from the line of action itsunitsr newton metre

Answer 2

Answer:

×1+x2/2,y1+y2/2

summation of p= summationof m×v cm

torque is the product of f and perpendicular distance of f from the line of action itsunitsr newton metre

Explanation: