Acceleration of a 2D circle due to Gravity.by clm222 Tags: circle geometry, gravity acceleration, inclined plane 

#1
Jul712, 08:21 PM

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Hello
Im wondering how to calculate the acceleration of a circle down an inclined plane (due to gravity). I am familiar with caclulating the acceleration of a body sliding down a inclined plane, but not a circle. How do you determine the acceleration of a circle (preffer rotation per second, if possible). I also would like to know how to calculate the fall of a topheavy object that has enough mass to fall, yes has a base on the ground (iea wooden plank with one end in the air, the other on the ground) 



#2
Jul712, 09:13 PM

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#3
Jul812, 02:16 AM

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Such an object acquires both linear velocity, v, and angular velocity, ω. Because it is rolling, these are related by v = rω. Likewise the accelerations, [itex]\dot{v} = r\dot{ω}[/itex]. There will be frictional force F acting up the plane. If the angle of the plane to horizontal is θ: [itex]m\dot{v} = mgsin(θ)  F[/itex] (resolving parallel to plane) [itex]M\dot{ω} = Fr[/itex] (moments about centre of object) where M is the moment of inertia of the object. For a thin ring that's mr^{2}; for a disc it's half that. You can solve between the three equations. It may even become airborne at some point. 



#4
Jul812, 01:11 PM

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Acceleration of a 2D circle due to Gravity.
Thanks, I'll have to learn 3D vectors/inertia/torque, I was planning to do so anyways, thank you




#5
Jul812, 09:42 PM

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Will the weight be acting on the top of the plank, or the center? Which do you usually use in physics?




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Jul812, 09:57 PM

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Jul812, 10:21 PM

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