Ball rolling down an incline angular and linear acceleration

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Homework Help Overview

The problem involves a ball rolling down an inclined plane, focusing on the relationship between linear and angular acceleration, with specific attention to the forces acting on the ball and its moment of inertia.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the net force acting on the ball, questioning the components of gravitational force along the incline. There is an exploration of the relationship between linear acceleration and angular acceleration, with attempts to derive expressions based on the forces involved.

Discussion Status

The discussion is active, with participants providing insights and checking each other's reasoning regarding the gravitational components and their implications for the ball's acceleration. Some guidance has been offered on the correct components of weight acting parallel to the incline.

Contextual Notes

There is an ongoing examination of the assumptions related to the moment of inertia and the conditions for rolling without slipping. Participants are also reflecting on the implications of their derived equations.

Fascheue

Homework Statement



A ball with moment of intertia bmr^2 rolls without slipping down a plane inclined at angle O. What is it’s linear acceleration?

Homework Equations



Fnet= ma

T = F x r

T = IO’’

a = rO’’

The Attempt at a Solution



Fnet = mgcos(O) - FfT = FfrT = IO’’

Ffr = bmr^2O’’

Ff = bmrO’’Fnet = mgcos(O) - BmrO’’a = O’’r

a/r = O’’Fnet = mgcos(O) - bma

ma = mg cos(O) - bma
a = gcos(O) - ba

a + ba = gcos(O)

a(1+b) = gcos(O)

a = gcos(O)/(1+b)
 
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Fascheue said:
Fnet = mgcos(O) - Ff
Check this: What is the component of the weight parallel to the plane?
 
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Doc Al said:
Check this: What is the component of the weight parallel to the plane?
Oops, would it be mgsin(O)?

I believe that would give an answer of gsin(O)/(1+b) following the rest of my steps.
 
Fascheue said:
Oops, would it be mgsin(O)?
Yep.

Fascheue said:
I believe that would give an answer of gsin(O)/(1+b) following the rest of my steps.
Looks good to me.
 
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