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Thread: The time frame deceleration for rolling bodies

  1. #1 The time frame deceleration for rolling bodies 
    ABV
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    On a straight track.
    Let say external friction force Ffr, no rolling resistance, initial velocity V0 moment of inertia I,
    Let's make a kinematic equation



    follow to



    and



    finally



    A solid disk's moment of inertia



    A ring's moment of inertia


    for thin ring R1 ~ R2



    Time for solid disk is




    Time for thin ring is






    I't means, force is same but time frame is different. Correct?
    If no, please provide a correct a kinematic equation and time frame formula.


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  3. #2 Re: The time frame deceleration for rolling bodies 
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    Quote Originally Posted by ABV
    On a straight track.
    Let say external friction force Ffr, no rolling resistance, initial velocity V0 moment of inertia I,
    Let's make a kinematic equation



    follow to



    and



    finally



    A solid disk's moment of inertia



    A ring's moment of inertia


    for thin ring R1 ~ R2



    Time for solid disk is




    Time for thin ring is






    I't means, force is same but time frame is different. Correct?
    If no, please provide a correct a kinematic equation and time frame formula.
    There seems to be something unstated in your formulation of the problem. A frictional force only exists in response to some externally appllied force. Otherwise the only force external to the rolling ring or disc as you suggest it, is the normal force of reaction from the surface on which it is rolling, in reaction to gravity.

    You cannot even state what the frictional force is, except in the case of impending slippage or in the case of sliding friction, in which cases it is defined by the normal force and the coefficient of friction.

    You need to either fully describe the problem or else start with a free body diagram that de facto defines the situation.


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  4. #3 Re: The time frame deceleration for rolling bodies 
    ABV
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    Quote Originally Posted by DrRocket

    You need to either fully describe the problem or else start with a free body diagram that de facto defines the situation.
    I'm sorry.
    The initial conditions are. No sliding on initial. The rolling body move without slipping. No rolling resistance. There is a flat surface, no inclines. I just want to see a behavior for rolling bodies with different moment of inertia.
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  5. #4 Re: The time frame deceleration for rolling bodies 
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    Quote Originally Posted by ABV
    Quote Originally Posted by DrRocket

    You need to either fully describe the problem or else start with a free body diagram that de facto defines the situation.
    I'm sorry.
    The initial conditions are. No sliding on initial. The rolling body move without slipping. No rolling resistance. There is a flat surface, no inclines. I just want to see a behavior for rolling bodies with different moment of inertia.
    In that particular case there is no difference. If there is no incline, and no rolling friction the ring and the disk simply continue forever at whatever initial velocity you give them. The only external force in that case is gravity which is perpendicular to the velocity, directed through the CG, and is exactly countered by the reaction force of the surface on which they are rolling. No net external force and no torque about the center go gravity, so no change in anything. They just keep rolling along ....
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  6. #5 Re: The time frame deceleration for rolling bodies 
    ABV
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    Quote Originally Posted by DrRocket
    In that particular case there is no difference. If there is no incline, and no rolling friction the ring and the disk simply continue forever at whatever initial velocity you give them. The only external force in that case is gravity which is perpendicular to the velocity, directed through the CG, and is exactly countered by the reaction force of the surface on which they are rolling. No net external force and no torque about the center go gravity, so no change in anything. They just keep rolling along ....
    Sorry again.
    A simple one.
    A rolling body has an initial velocity V on flat surface without rolling resistance and without a slippery.
    An External force. Letís say a small human on the surface holding a rolling body axis and try to stop it with force Ffr.
    He tried twice with different rolling bodies. These rolling bodies have a different moment of inertia. It means a different full kinetic energy.
    Would these rolling bodies have different distance and time?
    Would human gains different momentums to the surface?
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  7. #6 Re: The time frame deceleration for rolling bodies 
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    Quote Originally Posted by ABV
    Quote Originally Posted by DrRocket
    In that particular case there is no difference. If there is no incline, and no rolling friction the ring and the disk simply continue forever at whatever initial velocity you give them. The only external force in that case is gravity which is perpendicular to the velocity, directed through the CG, and is exactly countered by the reaction force of the surface on which they are rolling. No net external force and no torque about the center go gravity, so no change in anything. They just keep rolling along ....
    Sorry again.
    A simple one.
    A rolling body has an initial velocity V on flat surface without rolling resistance and without a slippery.
    An External force. Letís say a small human on the surface holding a rolling body axis and try to stop it with force Ffr.
    He tried twice with different rolling bodies. These rolling bodies have a different moment of inertia. It means a different full kinetic energy.
    Would these rolling bodies have different distance and time?
    Would human gains different momentums to the surface?
    This one is a a bit more complicated. Both rings, since they if the same material and weight will allow the same maximun frictional force at impending slip. That frictional force will be in the direction of motion, opposing the decelaration of the force being applied to the axle and creating a torque that reduces the initial angular velocity. This means that the free body diagram for the two rings are the same, assuming impending slip. But because you have a dynamic situation the condition of no slip implies a constraint between translational speed and angular speed. Which limits the allowable rate of deceleration.

    This is more easily analyzed using energy considerations, but the bottom line will be that with the same initial speeds the ring with the higher moment of inertia will have greater initial rotational energy and it iwll take more distance and longer time to decelerate it without slip -- all of that energy goes into work done on the extermal system that is trying to stop it.
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  8. #7 Re: The time frame deceleration for rolling bodies 
    ABV
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    Quote Originally Posted by DrRocket

    This one is a a bit more complicated. Both rings, since they if the same material and weight will allow the same maximun frictional force at impending slip. That frictional force will be in the direction of motion, opposing the decelaration of the force being applied to the axle and creating a torque that reduces the initial angular velocity. This means that the free body diagram for the two rings are the same, assuming impending slip. But because you have a dynamic situation the condition of no slip implies a constraint between translational speed and angular speed. Which limits the allowable rate of deceleration.

    This is more easily analyzed using energy considerations, but the bottom line will be that with the same initial speeds the ring with the higher moment of inertia will have greater initial rotational energy and it iwll take more distance and longer time to decelerate it without slip -- all of that energy goes into work done on the extermal system that is trying to stop it.
    Thank you for answer. If time is different and same decekeration force same in both cases.
    P=F*t
    Does it mean this a little human gains a different momentum ito the surface in this two cases?
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