I am very confused by the following problem asked in my first year physics class:
Please let me know if you can assist in any way! I've spent hours and hours on this question and gained absolutely nothing. Everything I do seems to lead to a contradiction one way or another.
There are other resources online I've found that mention this question, but I can't tease out a good solution from these: Force on a solid cylinder that is rolling on an accelerating block https://www.physicsforums.com/threads/a-rolling-disc-on-a-slab.594918/
Thank you!
Answer
As this is a homework question I won't give you a full solution, only point you in the right direction.
On the lower block acts a second force, $F_F$, a friction force that causes torque and the angular acceleration $\alpha$ of the cylinder:
$$F_F R=-I\alpha$$
Where $I$ is the moment of inertia of the cylinder and $R$ its radius. It carries a minus sign because it points in the opposite direction of $F$.
So the net force acting on the block is:
$$F_{net}=F-F_F$$
Now also note that for rolling without slipping, with $a$ the acceleration of the block, then:
$$a=\alpha R$$
To determine $a$ and $\alpha$ use the equations above to set up:
$$F_{net}=ma$$
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