For any disk with a no-slip contact point, c, in contact with a stationary object, is it ever possible for the contact point, c, to have an acceleration in a direction other than towards the center of the disk?
I know that if the disk is released from rest, the acceleration towards the center will be zero.
So does this mean that the acceleration of the contact point in any direction would be zero if released from rest?
2 comments:
If you look at the rigid body equation the (alpha) x R component will always give you an acceleration perpendicular to the radius.
This is the acceleration the friction force cancels out so I believe what you said holds true.
Agreement all the way around here. No slip means that the contact point acceleration must have a zero component along the surface on which it does not slip (usually, that is called "x"). Therefore, all that is possible is a "y" component. If it is a circular wheel, then this means that the acceleration of the contact point is directed toward the center of the wheel.
As you have noted, this y-component of acceleration is zero if the disk is at rest (omega = 0).
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