Week 8 - Angular Kinematics and Kinetics

angular displacement

change in absolute angular position

position units (linear)

m

position units (angular)

rad or °

displacement units (linear)

m

displacement units (angular)

rad or °

velocity units (linear)

m/s

velocity units (angular)

rad/s or °/s

acceleration units (linear)

m/s²

acceleration units (angular)

rad/s² or °/s²

what is an angle

orientation of two lines, two planes, a line and a plane, two segments, etc in relation to each other

angular displacement formula

Ʃθ = θf - θi

angular displacement

degrees and radians

radians formula

θ = arc length/ r

angular velocity

rate of change of angular displacement

angular velocity formula

ω = (θ2 − θ1)/∆𝑡𝑖𝑚𝑒

angular acceleration

rate of change of angular velocity

angular acceleration formula

α = (ω2 − ω1)/ ∆𝑡𝑖𝑚𝑒 → rad/s² or °/s²

resistance to linear acceleration

mass

resistance to angular acceleration

moment of inertia

What directly influences moment of inertia

mass and the distribution of mass, relative to axis of rotation

if you are ____ to the midline, the moment of inertia is _____

closer; smaller

body segments have ______ axes of rotation and moments of inertia for each ______ ____ _______.

different; plane of motion

moment of inertia formula

𝐼 = 𝑚𝑘² = 𝑚(𝜌𝑙)² → kg*m²

radius of gyration (k)

the distance from the axis of rotation to a point where the body’s mass could be concentrated without altering its rotational characteristics

radius of gyration represents segment’s _____ ______ about axis of rotation and _____ from axis of rotation to point assumed where mass is concentrated

mass distribution; distance

angular momentum

iw

factors that affect angular momentum

• mass of the object (m)

• distribution of mass relative to axis of rotation (k)

• angular velocity of the object (w)

newtons first law

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

conservation of angular momentum

if no external forces act on an object, then i1w1-i2w2

newtons second law

a net torque produces angular acceleration of a body that is directly proportional to the magnitude of the torque, in the same direction as the torque, and inversely proportional to the body’s moment of inertia

newtons third law

for every torque exerted by one body on another, there is an equal and opposite torque exerted by the second body on the first