Chapter 9 -Centre of Mass, Linear Momentum and Collisions

The good news about this image is it shows a real-life example of Momentum and impulse (Change in Momentum) , and it falls under the category of PARTIALLY ELASTIC COLLISIONS (read full course).

(And the bad news? Look closely, the batsman’s right foot is in-between the stumps, and can lead to a hit-wicket ! An AI problem. But it doesn’t 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