KINS 4200 Exam 3 Angular Kinetics I

angular kinetics

motion around an axis of rotation

angular motion

all parts of body do not move through same distance during same amount of time

kinetics

forces that cause the motion

torque formula

torque = force x moment arm

torque definition

tendency of a force to cause rotation about an axis

unit: Nm

torque directions

counterclockwise = +

clockwise = -

line of pull/action

straight line in the direction of which the force is acting

muscle force occurs along

the line of pull/action

moment arm definition

perpendicular distance from the line of action of a force to the axis

calculating moment arm

r_t = r x sin(θ)

• r = distance from axis to muscle insertion

joint angle influences moment arm

moment arm changes non-linearly with joint angle

center of mass definition

point about which the sum of torques is equal to zero

point around which a body’s mass is evenly distributed

center of gravity definition

the projected position of the COM vertically on the ground

COM does NOT equal COG

calculation of gravitational torque

torque = force x moment arm

force = mass of object x (-9.81)

calculating COM formula

solving for coordinates

m₁gx₁ + m₂gx₂ + … = Mgx_cm

m₁gy₁ + m₂gy₂ + … = Mgy_cm

1st law: law of inertia linear

body will maintain a state of constant velocity unless acted on by an external force

inertia definition

tendency of a body to resist a change in tis state of motion

1st law: law of inertia angular

body will maintain a state of constant rotational motion unless acted on my an external torque

moment of inertia

body’s resistance to a change in angular motion

depends on mass and distribution of mass with respect to the axis of rotation

law of inertia in static system

if ΣT = 0, then Δw = 0

static system, sum of torques = 0