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Suppose a sphere is rolling on the ground and there is friction. Friction is the only net force acting on it, and by newton's law, it will accelerate the object in the direction of the force (which is backwards). But the object is actually accelerating forward because friction is generating a positive torque.

Some equations:

Acceleration of center of mass = radius * angular acceleration (pure rolling motion)

Torque = radius x Force

Torque = moment of inertia * angular acceleration

Solving for acceleration of center of mass, I get two different answers. It seems that torque takes into account of the fact that the moment of inertia of a sphere is 2/5 mr^2 but newton's second law doesn't. How to account for the differences? Am I doing something wrong?

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# Newton's second law F=ma and torque do not agree?

Can you offer guidance or do you also need help?

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