AP Physics 1- Unit 4: Linear Momentum

4.1 Linear Momentum

All objects have momentum, even if it is 0

Momentum is a vector quantity described by;

$p=mv$

Unit: $kg m/s$

4.2 Change in Momentum and Impulse

Change in momentum will occur if an external force is applied

If no external forces are applied, momentum does not change

Impulse: change in momentum

Momentum: quantity of motion, how hard it is to stop a moving object

$J=p_f-p_i$

Impulse can also be represented as the area under a force vs time graph

$J=F\Delta t$

Unit: $N/s$

Impulse-Momentum theorem:

The impulse applied to an object will change its momentum

4.3 Conservation of Linear Momentum

An isolated system has a constant momentum

Momentum is conserved

Momentum of the whole system is found by adding the momentums

Velocity of the system can be found by looking at the common point (only if they share the same $v_i$

If the system does not have the same $v_i$, you can find the velocity by;

$v_{\operatorname{cm}}=\frac{\sum p}{\sum m}=\frac{\sum mv}{\sum m}$

4.4 Elastic and Inelastic Collisions

Momentum is conserved in all internal interactions

The total momentum within a system is constant only if its net external force $=0$

When a net external force is applied on a system, momentum is transferred between the system and the enviroment

There are 2 types of collisions:

    1. Elastic collisions

The total kinetic energy of the system stays the same before and after the collison

The objects in the collision do not stick

$KE_i=KE_f$
    2. Inelastic collisons

The total kinetic energy of the system decreases during the collision

The energy is transferred into thermal or sound energy

KE_i>KE_f