Chapter 9 -Centre of Mass, Linear Momentum and collisions

The good thing about this image is it shows something about momentum and impulse.

(And if  you look very closely, the batsman’s foot is in-between the stumps! That’s not exactly a good thing. anyway this is only an observation, it doesn’t affect learning about Momentum and Impulse.)

Momentum of the Bat & ball as a SYSTEM, taken together is CONSERVED at the moment of impact . Momentum of the bat is exactly transferred to the ball . Bat having a much higher mass, lower velocity of course, transfers its momentum to the Ball having a much lower mass, thus the ball flies at a high velocity. Energy of the collision is conserved.

The equations for Momentum and Impulse, have nothing to do with any loss of energy at the time of Impact. [losses like thermal energy loss , sound energy emitted of bat hitting the ball, compression of the ball and so on]

In almost all the real life collisions, there will be a loss of energy , we can hear the sharp thud of bat hitting ball, and the ball’s temperature will rise very slightly.

Let’s look at the various topics covered in this course:-

1) Get a feel for the concept of Momentum and Collisions – practical example of a ball dropped on the floor and rebounding.

2) Center of Mass : what is it

3) Uniform Mass Density

4) Equation derivation of center of mass for a Uniform Straight Rod

5) Linear Momentum and Conservation of Momentum

6) Collisions types :

• Elastic/perfectly elastic
• Inelastic
• Partially Inelastic – the majority of real-world cases fall in this category
• Co-efficient of Restitution – measure of relative velocity of Approach versus Relative velocity of Separation of objects

7) Elastic Collision: animation of a ball hitting another ball , storing and release of potential energy

8) Collisions -special cases

• heavy object hits a very light object
• light object hits a stationary Heavy object

9) Perfectly Inelastic collisions: animation of ball hitting another ball

10) Partly Elastic and Partly Inelastic Collisions

11) Moving Block colliding with a stationary Spring : animation and explanation

12) Co-efficient of Restitution

13) Elastic collision in more than one dimension: animation :- ball falling into spherical cup

14) Solved Problems