1. The problem statement, all variables and given/known data We have a system, consisting of a Disk radius R, with weight M, with a cordless string attached on its edge, at one edge of this cordless string we have a block of mass m, at the other end, we have the string attached to a spring with one end fixed to the floor, with spring constant k, also, the disk is on an axle, so it's mid air, and their is no friction between the disk and the axle. What is the max velocity of the block? 2. Relevant equations Let's say the positive y direction is downward, we have the string to spring on the left, and the block of mass m attached to the right which will be released (at which the spring will also be in the relaxed state) so we choose the direction of the angular velocity to be clockwise, (towards suspended block) Fnet y of spring: T1 = kx Fnet y of Disk: T1 + T2 + Mg - N (axle on disk) = 0 Fnet y of block mass M: mg - T2 = may tau (net) = T2R - T1R = Ialpha Vy^2 = Voy^2 + 2ay (delta y) 3. The attempt at a solution We can find the acceleration of the block, by relating it with the following atan = ay = alphaR Thus alpha = ay/R Substituting alpha in Tau net we get T2R - T1R = MR^2(ay/R) ==> ( I used I = MR^2) , cancellation of R and solving for T2 = May + kx (I put T1 = kx) Plugged this in for Fnet of block mg - (May + kx) = may My result for ay = (mg - kx)/ (m + M) , now I can use Vy^2 to solve for a V but I get an equation in terms of X, m, M, g, K, and H (delta y) how do i go about finding Vy max of block with Voy = 0, at what point is the force of spring and force of w of block such that the block has a max v? My result ( I think it's wrong or I'm missing something) Vy = sqrt( 2ayh) using ay derived above.. What am I missing to find the max Vy of block? What roles do mg and kx play in control of blocks speed, angular speed, and distance H displaced by block, also how can I relate delta x of spring (sorry I just realized its a bad idea to use x in kx, since we are only dealing with y dir. My apologies.) with the change in H of block? Can you? Thanks I advanced!