impulse on a secret mission… … to change equilibrium states!

IMPULSEOn a secret mission…

… to change equilibrium states!

We have seen that…

… equilibrium is a self-sustained state;


… equilibrium is a self-sustained state;… objects in equilibrium will remain so indefinitely, unless acted upon by an agent;


… equilibrium is a self-sustained state;… objects in equilibrium will remain so indefinitely, unless acted upon by an agent;… there are two categories of equilibrium: static (object @ rest) and dynamic (object in uniform motion);


… equilibrium is a self-sustained state;… objects in equilibrium will remain so indefinitely, unless acted upon by an agent;… there are two categories of equilibrium: static (object @ rest) and dynamic (object in uniform motion);… each equilibrium category is further broken into types;

We have seen that… (cont’d)

… static equilibrium types are mutually exclusive, whereas dynamic types are mutually inclusive;


… static equilibrium types are mutually exclusive, whereas dynamic types are mutually inclusive;… the ability of an object to retain its state of equilibrium is called inertia;


… static equilibrium types are mutually exclusive, whereas dynamic types are mutually inclusive;… the ability of an object to retain its state of equilibrium is called inertia;… inertia is the degree of “laziness” or “resistance” to change;


… static equilibrium types are mutually exclusive, whereas dynamic types are mutually inclusive;… the ability of an object to retain its state of equilibrium is called inertia;… inertia is the degree of “laziness”, or “resistance” to change;… while in equilibrium, an object’s motion is due to inertia;


… each category of equilibrium is associated with a distinct type of motion;


… each type of equilibrium is associated with a distinct type of motion;… objects in static equilibrium are at rest, and thus their position is constant;


… each type of equilibrium is associated with a distinct type of motion;… objects in static equilibrium are at rest, and thus their position is constant;… objects in dynamic equilibrium are in uniform motion, and thus their velocity is constant.

In summary…STATIC EQUILIBRIUM• Object is at rest;

DYNAMIC EQUILIBRIUM• Object is in uniform

(translational and/or rotational) motion;


• Object’s position is constant;



• Object’s (linear and/or angular) velocity is constant;

In summary…STATIC EQUILIBRIUM• Object is at rest; • Object’s position is constant;

• The three types (stable, unstable and indifferent) are mutually exclusive;




• The two types (translational and rotational) are mutually inclusive;


• Object’s position is constant;

• The three types (stable, unstable and indifferent) are mutually exclusive;

• Measure of inertia: mass (for translations) or moment of inertia (for rotations)

DYNAMIC EQUILIBRIUM

• Object is in uniform (translational and/or rotational) motion;


• The two types (translational and rotational) are mutually inclusive;

• Measure of inertia: momentum (linear, for translations or angular, for rotations)

Change!• Any change in equilibrium requires an agent.

Change!• Any change in equilibrium requires an agent.• To change between states, the object must

change its momentum!


change its momentum!• Changes involve a difference between a final

state and an initial state:(final state) – (initial state) = change in state


change its momentum!• Changes involve a difference between a final

state and an initial state:(final state) – (initial state) = change in state

• “Change in” in Physics (math) is represented by the Greek letter “uppercase delta”:

(change in variable) ≡ Δ (variable)

Change! (cont’d)(final state) – (initial state) = change in state




REPRESENTATION:Initial state: subscript “1”Final state: subscript “2”



REPRESENTATION:Initial state: subscript “1”Final state: subscript “2”

Δ (variable) = (final value)2 – (initial value)1

For example…

• Change in temperature T:Δ T = T2 – T1

For example…


• Change in mass m:Δ m = m2 – m1

For example…


• Change in mass m: DENOTES A VECTOR

Δ m = m2 – m1

• Change in (linear) momentum p:Δ p = p2 – p1

The Role of IMPULSE in TRANSLATIONS

• IMPULSE is, by definition, the change in linear momentum:


• IMPULSE is, by definition, the change in linear momentum:

(Impulse and momentum are vectors)

ARROWS REPRESENT VECTORS


• IMPULSE is, by definition, the change in momentum:

(Impulse and momentum are vectors)

• IMPULSE is the “argument” used to convince the object to change its state of equilibrium.


• IMPULSE is, by definition, the change in momentum:

• IMPULSE is the “argument” used to convince the object to change its state of equilibrium.

• Impulse depends on the “strength of the argument”, and the “length of the speech”.


LANGUAGE ARTS

• Strength of argument:

PHYSICS (MATH)

• FORCE


LANGUAGE ARTS

• Strength of argument:

• Length of speech:

PHYSICS (MATH)

• FORCE

• INTERACTION TIME Δt

IMPULSE EQUATION

• Both strength and length of speech must be present for a (meaningful and certain) sway in opinion to take place.

IMPULSE EQUATION


• Both force and interaction time must be present for a (measurable) change in linear momentum to take place.

IMPULSE EQUATION


• Both force and interaction time must be present for a (measurable) change in linear momentum to take place.

• “Both being present” means “AND”

IMPULSE EQUATION


• Both force and interaction time must be present for a (measurable) change in momentum to take place.

• “Both being present” means “AND”• “AND” in math translates into “multiplication”

IMPULSE EQUATION

impulse on a secret mission… … to change equilibrium states!

Documents