- #1

GemmaN

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It looks like your standard matchbox car loop.In this problem you will consider the motion of a cylinder of radiusr_1that is rolled from a certain heighthso that it "loops the loop," that is, rolls around the track with a loop of radius r_2. The cylinder rolls without slipping.

I need to find the minimum height

*h*that will allow a solid cylinder of mass

*m*and radius

*r_1*to loop the loop of radius

*r_2*. "Express h in terms of the radius r_2 of the loop."

I am not quite getting a certain portion of this. I know the important part of this problem is when the cylinder is at the top of the loop.

Now, at this point, I know it has a potential energy of 2*r_2*m*g

To stay on the track without slipping, I think I need v = R*omega

At the top part of the track, the cylinder is upside down, and has no normal force... so weight matters?

I may need to use this: K = 1/2Mv_cm^2 + 1/2 I_cm*omega^2

mgh = (2)r_2(mg) + KE? + ?

I am a bit confused at this point. How am I suppose to put this together?