Rotation Bodies - rolling cylinders

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November 12th 2009, 01:28 PM
jddery

Rotation Bodies - rolling cylinders

Every year at Coopers Hill in Gloucestershire (UK) there is a cheese rolling festival where people race down the hill after a rolling disc of Gloucestershire cheese, the winner getting to keep the cheese. (No, I'm not kidding look here. It seems there will even be an event in Whistler, BC next year if you are really interested.)

Given that the moment of inertia of a disc of mass m and radius r about its axis of symmetry is http://moodle.phys.ualberta.ca/filte...86e3542fc6.gif, what is the speed of the cheese's centre of mass after it has descended a vertical distance of 17.0 m from the top of the hill? Assume that the cheese rolls without slipping.
[Acceleration due to gravity, g=9.81 ms-2]

[Specify your answer in units of 'm/s' (without quotes)]
November 12th 2009, 03:53 PM
skeeter

Quote:

Originally Posted by jddery

Every year at Coopers Hill in Gloucestershire (UK) there is a cheese rolling festival where people race down the hill after a rolling disc of Gloucestershire cheese, the winner getting to keep the cheese. (No, I'm not kidding look here. It seems there will even be an event in Whistler, BC next year if you are really interested.)

Given that the moment of inertia of a disc of mass m and radius r about its axis of symmetry is http://moodle.phys.ualberta.ca/filte...86e3542fc6.gif, what is the speed of the cheese's centre of mass after it has descended a vertical distance of 17.0 m from the top of the hill? Assume that the cheese rolls without slipping.
[Acceleration due to gravity, g=9.81 ms-2]

[Specify your answer in units of 'm/s' (without quotes)]

use energy principles ...

$mgh = \frac{1}{2}mv^2 + \frac{1}{2}I \omega^2$

remember that if the disk rolls w/o slipping, $v = r\omega$
November 12th 2009, 05:36 PM
jddery

hey how would we get the answer of this question with out knowing the radius?
November 13th 2009, 04:43 AM
skeeter

Quote:

Originally Posted by jddery

hey how would we get the answer of this question with out knowing the radius?

the radius is not necessary ... do the algebra and see why for yourself.
November 17th 2009, 05:21 AM
nukaie

I based this question off of the time dilation

and since they are saying its at rest
would I assume that v^2/c^2 is zero?
and simply the equation is 2.2 micro seconds/ 1?

And

http://www.mathhelpforum.com/math-he...73c2a4fdb8.png

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