1. The problem statement, all variables and given/known data Hi everybody! Still checking my comprehension of physics, and hopefully those posts will help other users! A homogeneous wooden sphere with mass M and radius R rotates about a perpendicular axis going through its center of mass. At the top of this axis is a homogeneous metal bar of length 2R and of same mass M. A massless string is rolled around the ball (see attached picture) and on its other end goes through a wheel and has a suspended mass attached to it. There is no friction. a) calculate the moment of inertia of the system wooden ball-metal bar regarding its rotation axis. The bar should be considered as infinitely thin. The moment of inertia of a sphere is JK = (2/5)MR2. b) what is the acceleration of the mass m in the field of gravity of Earth? c) what is the velocity of the mass m when it has gone down a distance h? 2. Relevant equations Moment of inertia, torque, Newton 2nd and 3rd laws, conservation of energy 3. The attempt at a solution Though it is not the hardest problem, I find the calculations messy and the risk of missing something high. Here is what I've done: a) First I calculate the moment of inertia of the bar: JS = (1/12)M(2R)2 = ⅓⋅MR2 ⇒ Jtotal = (2/5 + ⅓)MR2 = (11/15)MR2 Im pretty sure I can add the moments of inertia that way since they have the same axis of rotation, right? b) By Newton's 3rd law I know that the force of tension of the string on the mass is equal to the force of tension of the string on the sphere. I try to find an expression for T using the torque and the angular acceleration: Στ = T⋅R ⇒ α = Στ/J = 15T/11M The angular acceleration is also equal to tangential acceleration/radius aT/R, and in that case aT = a (the acceleration of the suspended mass): ⇒15T/11M = a/R ⇒ T = 11aR/15M I plug that into the Newton's 2nd law: a = ΣF/m = g - 11a⋅m⋅R/15M ⇒ a = g/(1 + 11m⋅R/15M) c) For that part I set up an equation of conservation of energy. I assume that the system starts at rest: m⋅g⋅h = ½⋅m⋅v2 + ½⋅J⋅ω2 Is that correct? I have a little doubt about the rotational energy. Then I substitute ω by v/R. Here again I have a little doubt: I allow myself this substitution because I think the velocity of the string at the sphere should be the same as the velocity at the mass. Anyway that gives me for the velocity: v = √(2⋅m⋅g⋅h/(m + 11M/15)) What do you guys think? It's always a bit tricky not to misjudge such a situation.. Thank you in advance for your answers! Julien.