If a block sliding on a low-friction surface suddenly hits a high-friction surface, it will topple over (if the friction is high enough). Unless I'm mistaken, the axis of rotation is the block's leading lower edge. In the block's reference frame, this is due to the fictitious inertial force acting at the center of gravity, providing a torque about the leading edge. However, in the inertial frame, the force is friction, acting on the bottom of the block. My understanding is then that there would be no torque, as the force would be directly through the axis. Clearly I'm misunderstanding something, so what is it?
I initially realized my lack of understanding in the context of cars rolling over on sharp turns but thought the block would be simpler because there are only two frames to worry about, with a simpler transformation between them.
Answer
My understanding is then that there would be no torque, as the force would be directly through the axis. Clearly I'm misunderstanding something, so what is it?
A torque isn't needed to make the block tip over. The block has non-zero angular momentum with respect to where the leading edge of the block suddenly comes to a rest. You are correct that a force applied at that edge exerts zero torque on the block. No torque means angular momentum is conserved (at least briefly), making the block start tipping. Now a new torque arises, which is gravity. If the block wasn't moving fast enough, the block will tip up a bit only to fall back over. If the block was moving fast enough, it will tip. And then maybe tip again. And again. Eventually friction will bring it to a stop.
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