ENS 306 Exam 2

center of gravity (COG)

imaginary point around which body’s weight is equally balanced in all directions; same as center of mass (COM); where force of gravity (weight) vector acts; point serves as index of total body motion

linear motion

translation of a system’s COG along an axis

angular motion

rotational movement of a system about an axis

angular motion case 1

system restricted by linear joint forces at joint center

angular motion case 2

system not restricted by linear forces

with no net forces to restrict motion, an object will:

rotate about COG

anthropometry

science that defines physical measures of a person’s size, form, and functional capacities; interested in the normal anthropometric measurements and variation of these measurers; important for biomechanics, ergonomics

anthropometry helps us answer:

where is the COG? how is mass distributed relative to the COG? anthropometry lookup table lists these values for whole body and each body segment

whole body P_COG depends on:

the distribution of weight among and within body segments

P_COG can be located:

outside the body

during angular motion, all points on object:

move in a circle about an axis of rotation; move through the same angle in the same time

angular kinematics

kinematics of objects or systems undergoing angular motion; described similarly as linear kinematic values

direction of angular motion

specify both axis and sign (CW/CCW)

right hand rule

point thumb in positive direction along axis of rotation; direction of curled fingers is positive rotation

counterclockwise (CCW) (right hand rule)

positive rotation

clockwise (CW) (right hand rule)

negative rotation

absolute angular position

fixed reference; reference lines usually vertical or horizontal

relative angular position

moving reference; joint angle

vector of angular position

magnitude - units of degrees or radians; direction - specify axis and sign

angular displacement

change in angular position of a segment or any point on the rotating segment

angular displacement formula

∆𝜃 = change in position, 𝜃_f = final position, 𝜃_i = initial position

vector of angular displacement

magnitude - units of degrees or radians; direction - specify axis and sign

radian

angular unit; 1 radian = angle subtended at the center of a circle by an arc equal in length to the radius; 𝜋 radians per 180°

1 radian in degrees

57.29°

angular velocity

the rate of change in angular position

angular velocity formula

𝜔 = angular velocity, 𝜃_f = final position, 𝜃_i = initial position, ∆t = change in time

vector of angular velocity

magnitude - units of rad/s or °/s; direction - specify axis and sign (𝜔 + if 𝜃 increasing, 𝜔 - if 𝜃 decreasing)

angular acceleration

the rate of change in angular velocity

angular acceleration formula

𝛼 = angular acceleration, 𝜔_f = final velocity, 𝜔_i = initial velocity, ∆t = change in time

vector of angular acceleration

magnitude - units of rad/s² or °/s²; direction - specify axis and sign (𝛼 + if 𝜔 increasing, 𝛼 - if 𝜔 decreasing)

slope of 𝜃 →

value of 𝜔

slope of 𝜔 →

value of 𝛼