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SI units : Kgms^{-1}

Momentum is a vector and so direction/sign must be considered

For the example below, both objects are moving in the opposite direction with the same speed. So one object has a positive velocity and the other one has a negative velocity

So when calculating momentum for each object, the sign of the velocity must be considered

Notice that one velocity is negative as it's moving in the opposite direction

To find the total momentum we just need to add both of them .

So really the sum is zero

Usually this refers to only one object

Change is the opposite of Sum

This is only for one object

For example a mass of 1kg moving at 2ms^{-1} rebounds with a velocity of 1ms^{-1}

Calculating the change in momentum

This can be applied for the above example.

As there is now a change in direction, the final Momentum is negative. This is because, the sign of the velocity is also negative(opposite)

So we just add it, why?

So now it's more negative so the change is in the opposite direction and greater in magnitude. However, "change" does not usually include the sign.

The sign is very important as it shows the BALL experiences a force in the opposite direction - this means for the change of momentum to be negative a resultant force must be in the opposite direction

And the ball exerts an equal and opposite force on the wall when rebounding

We already know the definition of force

Another word for change in momentum is Impulse and it is same as:

Just remember it like a push. When someone keeps pushing you for some time. Greater the push(force) and time. The more you fall!

So we can calculate the sum of the momentum of a system by adding the momentums together(considering the signs also)

This sum should then equal to the momentum after the collision

That's why we found, how to calculate the total momentum of a system

This is actually important so remember this!

We apply this law when making sure that the total momentum before and after the collision is the same

So we need to distinguish the difference between an elastic and inelastic collision:

- Elastic collision
- Inelastic
- If they say both share the same velocity, it means they are stuck together and the momentum is shared across the combined mass. This is always an inelastic collision
- Also momentum is always conserved and so is total energy of the system. Kinetic energy may not be conserved
- Same magnitude
- Opposite direction
- Acting on different objects
- Same line of action of force/ So no torque
- Same type of force
- Same magnitude of force
- Parrel and opposite
- They are separated by a perpendicular distance of s or d

There is an easier way to identify an elastic collision

To calculate relative speed, you should use a bit of logic. When two objects are moving in the same direction, then the relative speed is the difference. If they are moving in opposite direction, the relative speed is the sum of two velocities.

Remember that K.E is a scalar and so we just take the magnitude of the K.E of an object(excluding any signs)

Important points:

As we discus what it is, we will see how to identify the pairs

For example below, the gravitational force between planents are of the same type ,same magnitude and etc. Always remember the features above

They are very similar things however, applied in different situations

You must always sayperpendicular!

So you can either find the component of the force which is perpendicular to the distance (resolving), which is the easiest way - we followed the same method in energy but, in this the force must be perpendicular

Remember that moment is actually a vector and it has a direction - clockwise or anticlockwise

Like the above one -

The clockwise moment:

The anticlockwise moment:

As we know that the clockwise and anticlockwise momentum is equal we can:

So we can find the missing forces or missing distances

This can be used to do questions which state that the system is in equilibrium but, let's first see what center of gravity means!

Center of mass and gravity are two different things but, can be the same if the object is uniform and the same material all the way. This is used in gravitational fields(point masses)

So usually the center of gravity is the point where the weight of the beam is considered to act on

So you need to remember that the weight of the beam can be represented by a resultant force and this also must be considered in moment calculations

The two forces acting opposite to each other is called a couple

They have these characteristics:

So torque only gives turning effect, where as moment can give linear acceleration unless it's stopped by a pivot

The resultant force in a torque is zero but, not in equilibrium as it has a net moment or torque

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