System of Particles and rotation

  1. Define centre of mass.
  2. Where does the centre of mass lie if two particles are of equal masses?
  3. On which factors does the location of centre of mass depend?
  4. Prove that the centre of mass of two particles divides the line joining thw two particles in the inverse ratio of their masses.
  5. Distinguish centre of mass and centre of gravity.
  6. Obtain an expression for the position vector of centre of mass of a system of two particles.
  7. Torque and work, both are obtained as the product of force and distance. How do they differ?
  8. What is the geometrical meaning of angular momentum?
  9. Prove that the time rate of change of momentum is equal to the torque acting on it.
  10. Derive a relation between torque and angular momentum.
  11. State the law of conservation of angular momentum.
  12. Establish a relation between torque and angular acceleration. Hence define moment of inertia.
  13. Derive a relation between torque and moment of inertia.
  14. Derive an expression for the rotational kinetic energy of a rigid body rotating with an angular velocity w and hence define moment of inertia of the body.
  15. Why moment of inertia called so?
  16. Define radius of gyration.
  17. In a flywheel, most of its mass is concentrated towards its rim. Explain why?
  18. Give two examples to explain the principle  of conservation of angular momentum.
  19. If the earth suddenly contracts, what is the effect on the duration of a day?
  20. State the theorem of parallel axes and the theorem of perpendicular axes of moment of inertia.
  21. Derive expression for total kinetic energy of a rolling body.
  22. A ring, a disc and a sphere of same radius and mass rolls down an inclined plane from the same height h. Which one of these reaches the bottom (i) earliest, (ii) latest.
  23. What is the velocity of a body when it reaches the bottom of an inclined plane rolling without slipping?
  24. If the ice  on the polar caps of earth melts, how will it affect the duration of day?
  25. How will you distinguish a raw egg and a boiled egg by spinning it.
  26. Why is a ladder more apt to slip when you are high up on the ladder than when you have just started climbing?
  1. Determine the acceleration of a body rolling down an inclined plane without slipping. What is the minimum value of coefficient of friction required for the body to roll without slipping?
  2. State and prove the theorems of moment of inertia.