physics week 11 part 2 (ONLY SLIDES)

Total Momentum of a System

The sum of individual momentums.

Law of Conservation of Momentum

The total momentum of an isolated system is constant.

Impulse Approximation

An approximation where, during brief collisions and explosions with significant peak forces, other forces like gravity are neglected due to their comparatively insignificant impulse.

Center of Mass

A useful concept when dealing with multiple objects or parts of a single object, which can be thought of as the balancing point of the system.

What is the implication of the Law of Conservation of Momentum?

Interactions within the system do not change the system's total momentum.

What is the conclusion of the Law of Conservation of Momentum regarding events like collisions or explosions?

The total momentum of the system after an event is equal to the total momentum of the system before the event, although the momentum of each individual object may change.

Under what condition is the Law of Conservation of Momentum applicable to a system regarding external forces?

It applies to an isolated system where external forces are zero.

In the context of Impulse Approximation, what does P_i represent?

Momentum immediately before the event.

In the context of Impulse Approximation, what does P_f represent?

Momentum immediately after the event.

What happens to the momentum of the center of mass if there are no external forces acting on the system?

The momentum of the center of mass remains constant.

If the mass is constant and there are no external forces acting on the system, what can be said about the velocity of the center of mass?

The velocity of the center of mass is also constant.

Total Momentum Equation

$\text{Total Momentum} (P) = p1 + p2 + \ldots + pN = \sum{k} p_k$

Change in Momentum Equation

$\Delta P = \sum{k} \mathbf{F}{\text{ext on } k} \Delta t = \sum \mathbf{F}_{\text{ext}}$

Conservation of Momentum Equation (Constant)

$\Delta P = 0 \Rightarrow P = \text{constant}$

External Force in Isolated System Equation

$\mathbf{F}_{\text{ext}} = 0$

Initial and Final Momentum Equation

$Pi = Pf$

Center of Mass Position Equation

$\mathbf{r}{cm} = \frac{1}{M} \sum{j=1}^{N} mj \mathbf{r}j$