Velocity of a rolling body down an inclined plane

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Discussion Overview

The discussion centers around the calculation of the velocity of a rolling body as it descends an inclined plane, with a focus on the conditions affecting this motion, such as friction and air resistance. Participants explore theoretical aspects related to rotational motion and the forces involved.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant requests the formula for calculating the velocity of a rolling body down an inclined plane, asking for specific quantities involved.
  • Another participant questions whether friction and air resistance are factors in the scenario, indicating that more information is needed.
  • A different participant asserts that there is no friction or air resistance, framing the discussion within the context of rotational motion.
  • One participant argues that without friction, the body would slide rather than roll down the incline.
  • Another participant suggests that friction must be considered and mentions the radius of gyration as relevant to the discussion.
  • A request for further information is made, emphasizing the need for a complete question with all known variables.
  • One participant reiterates the absence of energy dissipation due to friction, suggesting that the focus should be on understanding the forces acting on the body and its rotational inertia.
  • Another participant provides an equation for the acceleration of a rolling body down the incline, expressing a desire to know the formula for the body's velocity upon reaching the bottom of the incline.
  • A follow-up question seeks clarification on whether the participant is asking for the equation of motion after the body has left the incline and is rolling on a horizontal surface.

Areas of Agreement / Disagreement

Participants express differing views on the role of friction and air resistance, with some asserting their absence while others argue for their consideration. The discussion remains unresolved regarding the specific conditions and formulas applicable to the scenario.

Contextual Notes

Participants have not reached a consensus on the assumptions regarding friction and air resistance, which may affect the calculations and understanding of the motion involved. The discussion also highlights the need for clarity in the problem statement and the variables involved.

roshan2004
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Can anyone tell me the formula of calculating the velocity of a rolling body down an inclined plane?Please state the quantities as well.
 
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Is there friction? Do we take into account air resistance? We need more information.
 
No there is no friction and air resistance.It's chapter is rotational motion.
 
If there is no friction then the body will not roll down the incline, it will slide.
 
I think we have to consider friction and the radius of gyartion is involved there.
 
Further information is still required. Please state the full question with all known information.
 
roshan2004 said:
No there is no friction and air resistance.It's chapter is rotational motion.
I suspect you mean that there's no energy dissipated due to friction, not that there's no friction. (No slipping.)

In any case, don't just go hunting for a formula; figure it out from basic principles. What forces act on the body? What's the rotational inertia?
 
I have been given the information about the acceleration of a rolling body down an inclined plane as
a=gsintheta/1+k^2/R^2
But I really want to know the formula of that body when it actually reaches down the inclined plane.
 
roshan2004 said:
I have been given the information about the acceleration of a rolling body down an inclined plane as
a=gsintheta/1+k^2/R^2
But I really want to know the formula of that body when it actually reaches down the inclined plane.
I'm not quite sure I understand, you want an equation of motion for when the body has left the inclined plane and is now rolling along a horizontal surface?
 

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