Graham Beasley

2022-07-21

Why in accelerated rolling, the center of mass must be at the origin of an inertial frame of reference in order for the second law to be applicable.

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losnonamern

Expert

Newtons $2$nd law only holds in an inertial frame.
If you use the center of mass of the rolling object as your frame of reference then the frame will be accelerating and $F=MA$ won't hold. However if you fix the frame of reference to a relatively stationary point, say the surface of the earth, it will.
Even in this case the frame is not truly inertial, but the acceleration is so small as to be insignificant.
An example often given is that if you are sitting in a bus and the bus is accelerating objects will appear to slide towards the back of the bus, even though no force is acting on them in that direction. What is actually happening is that the whole bus is accelerating forwards and the objects sliding backwards are actually at rest.

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