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andyrk
- 658
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Why don't we consider radial acceleration on the lowermost point in rolling without slipping?
No matter if friction is there or not. It is rolling without slipping and the conditions needed for that have been taken care of by the question/problem/examiner who made the question.(Though those conditions haven't been specified). And I didn't ask whether there would be any angular acceleration or not. I am talking about RADIAL acceleration that a particle executing circular motion experiences which is towards the centre (centripetal: centre seeking). So that's what I am saying. In rolling without slipping, the lowermost point is instantaneously at rest, but an instant later it has kicked back up and allowed a different point to come to the lowermost position. So why does the particle kick back up? Does it have something to do with the radial acceleration of the particle? Does the radial acceleration play any role in rolling without slipping or not?dreamLord said:Well, there is no force providing torque, so why should there be any angular acceleration? That is why I asked you to be specific - are you considering a situation where there is friction acting on the lowermost point or not?
andyrk said:I am talking about RADIAL acceleration that a particle executing circular motion experiences which is towards the centre (centripetal: centre seeking). So that's what I am saying.
Does the radial acceleration play any role in rolling without slipping or not?
voko said:Have you not answered your own question?
andyrk said:I don't think so because I still haven't come to a conclusion as of yet.
voko said:Yes you have. You stated quite plainly that anything in circular motion experiences radial acceleration.
andyrk said:Yes, what effect does it have on the lowermost point in contact with the surface? By the virtue of what does it kick back up while pure rolling?
But the radial acceleration of the lowermost point is straight back up normal to the surface. But the lowermost point moves diagonally upwards, i.e along the circular arc. Is it because while the lowermost point tends to move up, the rolling object is also rotating so it goes along the arc? Kind of like the Coriolis Effect?voko said:By the virtue of centripetal acceleration, just like you said.
andyrk said:But the radial acceleration of the lowermost point is straight back up normal to the surface. But the lowermost point moves diagonally upwards, i.e along the circular arc. Is it because while the lowermost point tends to move up, the rolling object is also rotating so it goes along the arc? Kind of like the Coriolis Effect?
haruspex said:andyrk, pls try to answer my questions in post #4. You will find that in an inertial frame the point of the wheel in contact is not accelerating.
Do the algebra. Suppose the point of interest is about to contact the ground. It still has an angle theta to go. If the radius of the wheel is r, what is its height from the ground? What does that approximate to for small theta? Writing theta = -ωt, constant ω, what does that give you for the vertical acceleration?andyrk said:The particle does experience radial acceleration at the lowermost point
haruspex said:Do the algebra. Suppose the point of interest is about to contact the ground. It still has an angle theta to go. If the radius of the wheel is r, what is its height from the ground? What does that approximate to for small theta? Writing theta = -ωt, constant ω, what does that give you for the vertical acceleration?
Remember, it has no centripetal acceleration since it has no tangential velocity.
No, it's r(1- cosθ). What does that approximate for small θ?andyrk said:Height of the point is r-rθ=r(1-θ)
Rolling without slipping is a motion in which an object, such as a wheel or ball, moves in a straight line while simultaneously rotating about its axis without any sliding or slipping.
The main difference between rolling without slipping and rolling with slipping is that in rolling without slipping, the point of contact between the object and the surface remains stationary, while in rolling with slipping, there is sliding or slipping between the two surfaces.
In rolling without slipping, the acceleration of the object can be calculated using the equation a = αr, where a is the linear acceleration, α is the angular acceleration, and r is the radius of the object. This means that the linear and angular accelerations are directly proportional to each other.
Yes, an object can still roll without slipping on an inclined plane as long as the force of friction between the object and the surface is sufficient to prevent slipping. The angle of the incline will affect the magnitude of the force of friction required to maintain rolling without slipping.
The distribution of mass in an object affects its ability to roll without slipping. For example, an object with a larger mass concentrated at its center of mass will have a lower moment of inertia and will be easier to roll without slipping compared to an object with a larger mass distributed farther away from its center of mass.