Chapter 9 -Centre of Mass, Linear Momentum and Collisions

Centre of Mass basically means the spot, or point where all the mass of any physical object is concentrated.

Let’s go to a wonderful far away planet , what a stunning background. I have placed a sphere, prism, cube, and rectangular block. The shining glowing spot inside denotes the centre of mass . It is an exxagerated illustration.

We will find the same equations there for Centre of Mass as we find on Earth, since mass remains the same for any shape irrespective of any planet where we might go. We are not talking about “weight” here. Only mass.

Below is a real-life image of Momentum

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 not-so-good news? Look closely, you will see the batsman’s right foot is in-between the stumps. This is not good and can lead to a hit-wicket if the bails fall off , a disaster ! But it doesn’t affect our learning of 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) Understand basic concept of Momentum and Collisions – practical example – ball dropped on the floor and rebounding.

2) Concept of Center of Mass

3) Centre of Mass – Objects having Uniform Mass Density – CUBE, BLOCK, SPHERE, PRISM, and generic PYRAMID

4) Center of mass for a Uniform Straight Rod – explanation of Integration

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) Collision in 2 Dimensions – Perfectly Elastic – 4 unknowns and 3 equations – indeterminate

13) Co-efficient of Restitution

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

15) Solved Problems