1. The problem statement, all variables and given/known data http://www.sumoware.com/images/temp/xzdmdjtlksnfhiqc.png [Broken] A solid ball rolls perfectly with initial velocity v0 in horizontal axis ( y-axis ) on an inclined plane with elevation angle Θ as the picture above shown. This ball moves turning due to the gravitational acceleration till it has traveled distance L in x axis when it's at the bottom of the plane. Determine the time (t) the ball needs to get to the bottom of the plane ! (The ball doesn't slip while rolling) 2. Relevant equations Rotational dynamics equation and linear kinematics equation Or conservation of energy equation 3. The attempt at a solution I have two methods to solve the problem. But, the answers are different. Using rot. dynamics equation and linear kinematics. I just consider the x-axis since it's what the question asks. ΣFx = ma mg sin Θ - f = ma (Note : f is friction force) f = mg sin Θ - ma Στ = I α f R = I α f R = I (a/R) (mg sin Θ - ma) R = (2/5) m R^2 (a/R) mg sin Θ - ma = (2/5) m a g sin Θ - a = (2/5) a (7/5) a = g sin Θ a = (5/7) g sin Θ Then, I use the kinematics equation L = 0.5 a t^2 2L/a = t^2 14L/ (5g sin Θ) = t^2 t = √(14L/5g sinΘ) But, using conservation of energy, I get different answer m g sin Θ L = (1/2) m v^2 + (1/2) I ω^2 m g sin Θ L = (1/2) m v^2 + (1/2) (2/5 m R^2) (v^2 / R^2) g sin Θ L = (1/2) v^2 + (1/5) m v^2 g sin Θ L = (7/10) v^2 v = √(10 g sin Θ L / 7 ) Then, I use the kinematics vt = vox + a t √(10 g sin Θ L / 7 ) = 0 + g sin Θ t t = √(10L/7g sin Θ) Which one is correct? Why?