Help with rotation/inertia problem

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Discussion Overview

The discussion revolves around a physics problem involving a ball rolling towards an inclined plane. Participants are exploring concepts related to kinetic energy, conservation of mechanical energy, and the effects of friction on the ball's motion as it transitions from a flat surface to an incline. The problem includes multiple parts that require calculations related to energy and velocity.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant asks for help with calculating total kinetic energy before the ball reaches the inclined plane, as well as subsequent velocities and distances after it leaves the incline.
  • Another participant notes that rolling without slipping simplifies the analysis, indicating that both rotational and translational kinetic energy must be considered.
  • A formula for total kinetic energy is proposed, involving the moment of inertia and angular velocity.
  • Conservation of mechanical energy is suggested as a method to find the linear velocity at the top of the incline.
  • There is a question about how to account for friction when the ball is moving up the incline, indicating uncertainty about its effect on energy conservation.
  • It is mentioned that if the ball rolls without slipping, static friction does not waste energy, implying that mechanical energy is conserved in this scenario.
  • A hint is provided regarding the relationship between angular velocity and translational speed for rolling objects.

Areas of Agreement / Disagreement

Participants generally agree on the application of conservation of mechanical energy in the absence of external forces, but there is uncertainty regarding the role of friction and how it should be incorporated into the calculations.

Contextual Notes

Participants express uncertainty about specific aspects of the problem, such as the treatment of friction and the application of energy conservation principles. The discussion does not resolve these uncertainties, and assumptions about the ball's motion and the nature of the incline remain implicit.

dimitri24
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lets say that:
a ball rolls on flat surface at a constant velocity towards an inclined plane

how would u answer the following, this is very confusing for me. i don't have the exact values =/

a)calculate KEtotal before it gets to the plane
b)calculate linear velocity when it makes it up to the top of the inclined plane
c)find out how far it falls after it leaves the inclined plane
d)and if the inclined plane were frictionless, would the ball's speed at the top of the incline be greater than, equal to, or less than the speed you already calculated

this is the best i can remember off the top of my head. any help is appreciated, thx
 
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Okay.Rolling without slipping surely makes life easier,metaphorically speaking.

U have a rigid body which undergoes both rotation & translation movement.What's the total KE...?

Daniel.

P.S.The problem doesn't say it explicitely,but u know the initial velocity & and the mass & the radius of the ball.
 
(1/2)(Icm)(w^2) + (1/2)(M)(Vcm^2) ?
 
Perfect.For point b),u need to apply the total mechanical energy conservation law.

Daniel.
 
im not familiar with that, is it easy to explain? thanks
 
Well,in the absence of any external forces,the total energy of the system formed by Earth & sphere is conserved (a theorem following from Newton's axioms).

Assuming the Earth to have an [itex]\infty[/itex] mass,this law can be written for the sphere only.

Intially u have KE and 0 PE,atop the ramp u have [itex]\neq 0[/itex] KE & PE.U know that the sum of both is the same,both at the botton of the ramp & atop.

Daniel.
 
but how do u account friction into the equation when the ball is going up the incline. how would i attack part b?
 
Well,energy is conserved in part b).So solve part b) and then worry about the friction on the incline.

Daniel.
 
dimitri24 said:
but how do u account friction into the equation when the ball is going up the incline. how would i attack part b?
Since the ball is assumed to roll up the incline without slipping, no energy is wasted doing work against friction. (It's static friction.) So, as Daniel says, mechanical energy is conserved.

Hint: What's the relationship between [itex]\omega[/itex] and the translational speed v when the ball "rolls without slipping"?
 

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