Normally for example in an inclined plane we have a circular disk that rolls down if the surface of the incline is rough (friction is present), this creates a torque that causes the ball to start rolling. However in my scenario we have a circular disk (or to be more specific a cable drum) from which a piece of rope/cable is pulled by some force horizontally to the right. Since there is no friction between the disk/drum and the ground (but there is still a torque created by the external force), would the disk rotate, and if so how? I would imagine that the disk would definitely rotate, but the "how" is more difficult.
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1How is the rope attached? A diagram might help quite a bit. – Jiminy Cricket. Jan 31 '23 at 23:26
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unfortunately I dont really know how to do that, but the rope would be attached at the edge of the disk, more specifically at the top. The force then pullls it to the right. – AB2 Jan 31 '23 at 23:27
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So, it pulls the top horizontally. It's not in-line with the centre of mass then. What do you think happens? – Jiminy Cricket. Jan 31 '23 at 23:45
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This might help - Toppling of a cylinder on a block – mmesser314 Feb 01 '23 at 05:02
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@JiminyCricket. Yes the disk would rotate, but what about the translation motion of the object? – AB2 Feb 01 '23 at 09:53
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Yes: apply both Newton's Second Law: $$ \vec{F}_{\rm net} = m \vec{a} $$ and Newton II for the rotation of a rigid body: $$ \tau_{{\rm net},\, z} = I \alpha_z $$ to see that: (1) your pulling force causes a horizontal acceleration (there are no other horizontal forces on the drum), and (2) your pulling force causes a net torque about, e.g., the center of the drum (there are no other torques on the drum). The magnitude of the force and the mass will determine the value of $a$, and those two together, along with the moment of inertia of the drum, will determine the value of $\alpha$. So if the drum starts from rest, it will later be sliding across the frictionless surface, while also rotating about its central axis.
The difference between this situation and the object rolling down an incline, is that here there is no connection between the rotational acceleration and the translational acceleration, i.e., there is no "rolling without slipping" condition.
Ben H
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