Static Equilibrium

static equilibrium

- all net forces/torques sum to 0
- static: not moving/moving at the same velocity + the acceleration = 0
- T=I(angular a) > no a > net external T = 0
- F=ma > no a > net forces sum to 0

Weight vs Mass

- Weight: force of gravity acting on an object; W = mass x gravity
- mass: how much matter we have (constant)

Force

- mechanical interaction between an object and its surroundings (the push or pull of one object on another)
- is a vector b/c it has magnitude, direction, + point of application

Acceleration

- change in velocity over change in time- units = m/s^2 or ft/s^2- you solve for acceleration to see if an object is speeding up/slowing down or changing direction- vector

Velocity

- linear (average) velocity: vector; time rate of displacement

Torque

- measure of extent to which a force will cause an object to rotate
- -forces that cause things to rotate
- Equations: T= force x mA / T= (mass moment of inertia) (angular acceleration)

Center of Mass

the point in a body or system around which its mass or weight is evenly distributed or balances and through which the force of gravity acts- human body COG= 1-2 inches below your navel

Anthropometry

- science that discovers how much body parts weigh in term of body percentage

Linear Motion vs. Angular Motion

- Angular Motion: all points in an object or system move in a circle about a single axis of rotation, needs a central point (axis) to rotate around
- linear motion: All parts of an object or system move the same distance in the same direction at the same time

Momentum

- momentum = how we describe / quantify motion **- equation: L=mv

Inertia

- the tendency to resist acceleration
- represented by mass (the greater the mass, the more force required to produce a given acceleration)

Mass Moment of Inertia

- For a single particle: Ii=miri^2- For an object: look at pic- mi = mass of particle i- ri = distance of particle i from axis of rotation- SI Units: kgm^2

Moment Arm (Lever Arm)

- perpendicular distance from a force's line of action to the axis of rotation
- axis = stick/hinge about which we rotate

External vs. Internal Force

- internal forces:
forces that act within the object or system whose motion is being investigated
- external forces: forces that act on an object as a result of its interaction with the environment surrounding it; examples:- contact forces: one object touches another (pushing/applying force on something)- non-contact forces: forces that occur even if the objects are not touching one another (ex: gravity)

are forces ever considered angular

- no, always linear
- force can only create an angular motion (=torque)

Internal vs External Torque

Internal Torque: muscles, ligaments, joint capsules, contact btwn bone (all occurs inside the body)- muscles have internal moment arms which create internal torque

External Torque: - gravity (weight)- wind/ push + pull from outside the body- external force > external moment arm > external torque- usually CW / neg

Vector

- mathematical tool that allows you to see quantities with magnitude, direction, + point of application
- velocity vs. speed (velocity has direction speed does not)

Static Analysis vs. Dynamic Analysis

- Static: deals with systems in a constant state of motion; sum of T=0 b/c there is no acceleration (T=f x ma)
- Dynamic: sum of T= net acceleration (T=MMOI X angular a)

if demand is > internal torque

if demand is < internal torque

- object moves in demand direction

- object moves in internal torque direction