[Physltest] [Phys-L] Re: rolling down an incline

[Herb Schulz <herbs@WIDEOPENWEST.COM>]

On 1/24/05 8:50 PM, "Herbert H Gottlieb" <herbgottlieb@JUNO.COM> wrote:

> A hollow brass pipe at rest is allowed to roll down
> to the bottom of a gentle incline without slipping.
>
> If the same pipe is then filled with a solid substance
> and the procedure is repeated, will it reach the bottom
> of the incline any faster?

Howdy,

I'd expect so. The acceleration of the cylinder of radius r (filled or
hollow) down the incline of angle theta without slipping is given by

 a = g*sin(theta)/(1 + R^2/r^2) where R is the Radius of Gyration of the
cylindrical object about its center (R^2=I/M, where I=Moment of Inertia
about the center and M=Mass of cylinder). E.g. For a thing walled hollow
cylinder R^2=r^2 so a = (1/2)*g*sin(theta) while for a ujniform solid
cylinder R^2=r^2/2 so a = (2/3)*g*sin(theta).

Good Luck,

Herb Schulz
(herbs@wideopenwest.com)
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