Hey guys, I am doing this problem:
A hollow cylinder is rollling on a horizontal surface with an initial speed of 3.6m/s when it reaches a 16deg incline. How far up along the incline does it go? How long will it take to reach its highest point on the incline?
Simple problem actually, It turns out there are two methods. The first method is to use conservation of energy, with a moment of inertia of MR^2.
That looks something like this:
mv^2=iw^2=2mgh
h=v^2/g
d=h/sin16 which gives you 4.8m. This is correct.
The time is also simple, you can use basic kinematics to solve for time, which looks a bit like this:
4.8=3.6t
t=2.67s.
We can even solve for acceleration
3.6=2.67a
a=1.35 m/s^2
Now, When we use the second method with torque, RxF=Ia.
This method, does not give me the magnitude of a with the first method.
rmgsin16=mr^2(a/r)
a=gsin16= 2.7m/s^2 which is precisely twice of what i should calculate.
This is because my moment of inertia should be mr^2+mr^2 (parallel axis theorem) instead of mr^2. But I don't understand why.
It has to do with the point of contact, but I don't understand it.