- #1
jti3066
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Homework Statement
A ball of mass 2.80 kg and radius 0.153 m is released from rest on a plane inclined at an angle θ = 41.0° with respect to the horizontal. How fast is the ball moving (in m/s) after it has rolled a distance d=1.60 m? Assume that the ball rolls without slipping, and that its moment of inertia about its center of mass is 1.80E-2 kg·m2.
Homework Equations
I = Icm + M(d^2)...parallel-axis theorem
wf ^2 = wi^2 + 2a(thetaF - thetaI)...constant angular acceleration
theta = S/r
v=wr
The Attempt at a Solution
I think I need to use the parallel-axis theorem to solve for one step in the problem, so...
I = 0.0180 + 2.8(1.6^2) = 7.186 kg * m^2
Next I found how many "radians" the ball travels in 1.6 m...
C = 2"pi"r = 2"pi" * .153m = .936 m (circumference of ball)
1rad = .936 m
1.6m * (1rad/.936m) = 1.7 radians
I am not even sure how to solve this problem...I did the above equations so I could see if I was going on the right track by a process of elimination...usually I don't worry about the actual numbers until the end of the problem...i.e. if I just use the units in the equations and my "answer" is in the correct units it usually means I am on the correct path...Please help me solve this problem...