   Moment of Inertia
  For any Math enthusiastsJust wonder if im doing this correct:the scenerio is a Dumbell.The weight of each ball (one on either end of the bar) is 2kg, and the radius of each ball is 15cm.the bar itself is 1 M long, and weighs 0.5kg.the bar is attached to the outside of the ball.both the ball and bar are hollow (shells).the system is being rotated along the Centre of gravity of the whole systemi know the equations for both objects are:(double letters means squared)r = radious of that objectm = massinertia of hollow bar = mrrinertia of hollow bar = 0.5*0.5*0.5inertia of hollow bar = 0.125now its the balls which are confusing me a little.inertia of hollow ball = 2/3 * mrrhowever, because we are rotating along the Centre of gravity (middle of the bar), do i need to add any extra bit so it looks like:d = distance from COG of ball, to the COG of the entire system.inertia of hollow ball = 2/3 * mrr + mddinertia of hollow ball = 2/3 * 2 * 0.15 *0.15 + (2*0.65*0.65)and because i have 2 balls, i just multiply by two, and add it to the Inertia of the bar. which gives me the final answer. is this correct?final answer = 1.875   
Quote:the system is being rotated along the Centre of gravity of the whole systemOn what axis? Is the dumbbell rotating in place (the axis being the axis of the bar), or is the thing revolving, with the sphere centers tracing out a circle?Quote:inertia of hollow bar = mrrOnly true if the dumbbell is rotating in place.Quote:because we are rotating along the Centre of gravity (middle of the bar), do i need to add any extra bitOnly if the dumbbell is revolving. Otherwise, the spheres are centered on the axis of rotation and d=0.   ;  sorry for that, in the practice exam paper this is what we are told:"Calculate the moment of inertia about the centre of gravity", which to me isnt very clear!i would assume they ment rotation through the Up axis. through the middle of the entire object------>l()-----------()my amazing image. the "l" is a string which the dumbell rotates about :P   ;  In that case, your calculation of the bar's moment is incorrect, but the calculation of the balls looks correct.   