Hi everyone, this problem involves smooth rolling and translational motion: 1. The problem statement, all variables and given/known data A bowler throws a bowling ball of radius R= 11 cm along a lane. The ball slides on the lane with initial speed vcom = 8.5 m/s and initial angular speed w0 = 0. The coefficient of kinetic friction between the ball and the lane is 0.21. The kinetic frictional force acting on the ball causes a linear acceleration of the ball while producing a torque that causes and angular acceleration of the ball. When speed vcom has decreased enough and angular speed w has increased enough, the ball stops sliding and then rolls smoothly. d)how long does the ball slide? 2. Relevant equations Flinear = ma = -mgμk torque = rF = Iα Ki + Ui = Kf + Uf 3. The attempt at a solution I have figured out the linear acceleration a = -2.1 m/s2, and angular acceleration α = 47 rad/s2 using the fact that Flinear = ma = -mgμk and torque = rF = Iα. I know that there is smooth rolling if vcom = rω = (.11m)ω I set up an equation using conservation of energy to solve for ωf, which is whenvsliding should end and smooth rolling should begin. (1/2)mvi2 + (1/2)I ωi2 = (1/2)mvf2 + (1/2) I ωf2 (1/2)m(8.5m/s)2 = (1/2)m(.11ω)2 + (1/2)(2/5 mr2)ωf2 Canceling out mass and simplifying: 36.125 m2/s2 = .00605ω2 + .00242ω2 ωf = 65.3 rad/s then, ω = ω0 + αt 65.3 rad/s = 47 rad/s2t t= 1.4 s However, the given answer in the book is 1.2s, and I'm not sure what's going on...I've tried to account for rounding errors, but that doesn't appear to be the problem. Am I neglecting friction when I shouldn't be, and if so, how would I calculate energy lost to friction if I don't yet know the distance the ball traveled? Any help would be appreciated, thank you.