MOI

moment of intertia is defined by the mass and distribution of that mass

angular momentom:

H = moment of inertia x angular velocity

H=Iw


H = Iw

clockwise = negative

anticlockwise = positive


I = mass x radius 2 (km.m²)

w = angular displacement / time (radians.s)

H = iw

degrees per second, you need to get radians per second before calculating the answer

radians don’t have dimensions


  • what is the angular momentum:

  • 6.5 and 6 radians

  • values shouldn’t be too high


angular velocity will be around 1- to 15

anfular momentum will be around 20 to 40


determine angular momentum of a body about a given axis

  • similar to method used determine moment of inertia about a given axis

  • parallel axis theorem: Ia = Icg + md²


angular momentum total:

H total = sum of all angular momentum


each segment has 2 parts

  1. segments about its own center of gravity

    1. IsWs/Gs +

  2. segment about the central axis

    1. Ms+R²WGs/G

Is = moment of inertia of segment about the axis through the segment CoG, Gs

ωs/Gs = angular velocity of the segment about the axis through Gs

ms = mass of the segment

r = distance between body CoG and segment CoG

ωGs/G = angular velocity of segment CoG about transverse axis through body CoG


moment of inertia = angular momentum / angular velocity

angular velocity = angular momentum/ moment of inertia


angular momentum: 39.68

angular velocity = 4 radians

mass on radius = 0.4

what is the mass of the performer=


moment of inertia / radius ²

39.68 x 4 = moment of inertia


158.72 × 0.4

= 63.488


H = I x W

39.68 = I x 4

39.68 = (m x r ²) x W

39.68 = m x (0.4²) x 4

39.68/(0.4²)/4

= 62 kg



a rotating body will continue to rotate with constant angular momentum unless acted on by an external moment

  • conservation of angular motion

determined at take off

cannot be changed once in the air


diver changed their moment of inertia to manipulate their angle of velocity

angular momentum remains constant

angular velocity will increase to maintain angular momentum constant

bringin mass close to the pivot increases velocity

moment of inertia is manipulated by athletes


once in flihgt no external force acting

an external moment produces an angular acceleration

sum of moment = moment of intertia x angular acceleration

directly proportional to the overall moment, inversely proportional to the moment of inertia of the object.


the rate of change of angular momentum is proportional to the moment (torque) causing it

moment = force x distance from the pivot


every action has an equal and opposite reaction

Example: During long jump, the long jumper raises their legs for clearance of the ground • This produces a lower body torque (moment)To counteract this, the arms and trunk are lowered producing an upper body torque (moment) • This is in the opposite direction

you cant generate rotational movement when you dont have access to other forces

Angular acceleration of lower and upper body are different - because moments of inertia are different - and angular momentum is conserved

angular momentum conserved because the inertia is so different, equal and opposite angular momentum

• When a body is in the air, total angular momentum is conserved (it always is!) • If the angular momentum of one part of the body is decreased, another part must increase to conserve total angular momentum






newtons seconds law

Angular momentum of a rotating body equals product of its moment of inertia and its angular velocity • H = Iω • Total angular momentum (H) of the body about the transverse axis through the CoG is the sum of angular momenta for all segments • HTOTAL = ΣHs • A rotating body will continue to rotate with constant angular momentum unless acted on by an external moment: - Conservation of Angular Momentum