How do you change an object's center of gravity so that it will roll uphill when placed on a 10 degree ramp?

Question

I need to know how to make an object that will rotate uphill with no force applied to it. It needs to be really creative and not the obvious....describe in detail please, because i already know the basics....

Answer 1

For my solution I chose a hollow cylinder of radius R, thickness p, and mass mc.

The way to get a cylinder to roll (any round object, for that matter), is to apply a mass, mp, at an angle th from the vertical axis so that
T=I alpha
where T is the torque and I is the moment of inertia, and alpha is angular acceleration. The application of the mp has changed the center of gravity such that the torque caused by mp in the presence of gravity (this is a natural force) rotates the cylinder.

In the case presented by this post, there is a torque on the cylinder due to its own mass when on an incline. This is because there is friction between the incline and the cylinder, so a force develops there.

What you want to do is to place mp on the cylinder an angle th from the vertical axis of the cylinder such that it is great enough to counter balance the torque created by gravity due to the mass of the cylinder.

Take care to decide where the angle th is. I chose th as an angle subtended by a vertical line from the center of the cylinder (in line with gravity), and a line fron the center of the cylinder to the mass that is applied. Note that I am treating mp as a point mass.

I summed the torques about the center of the cylinder as if the friction was exactly equal balanced and rotation up the slope is positive

The torque of the friction is
-(mc+mp)*g*sin(10)*r

The torque of the point mass is

mp*g*sin(th)*r

now to get the thing rotating, the torques must overcome the moment of inetia and create alpha
so,
mp*g*sin(th)*r>
(mc+mp)*g*sin(10)*r

or
mp/(mc+mp)>sin(10)/sin(th)

j